Skip to content
This repository has been archived by the owner. It is now read-only.
Permalink
bbe1e8a55d
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?

CodeSSN/Figure_2_characteristic_functions_and_steady states.nb

Go to file
 
 
Cannot retrieve contributors at this time
executable file 6219 lines (6170 sloc) 283 KB
Raw Blame
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 9.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 157, 7]
NotebookDataLength[ 289105, 6210]
NotebookOptionsPosition[ 287222, 6148]
NotebookOutlinePosition[ 287631, 6166]
CellTagsIndexPosition[ 287588, 6163]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{"Figure", " ", "2",
RowBox[{"(", "A", ")"}]}], ",", " ",
RowBox[{
RowBox[{"det", " ", "J"}], ">", "0"}], ",", " ",
RowBox[{"one", " ", "steady", " ", "state"}]}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Clear", "[",
RowBox[{
"Jee", ",", "Jei", ",", "Jie", ",", "Jii", ",", "ge", ",", "gi", ",", "n",
",", "te", ",", "ti", ",", "cplus", ",", "F", ",", "P", ",", "Z", ",",
"z0", ",", "re1", ",", "ri1", ",", "plot1", ",", "plot2", ",", "plot3",
",", "plot4", ",", "Ge", ",", "Gi"}], "]"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{"**", "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "********)"}],
"\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{"SSN", " ", "parameters"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**"}], "********)"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Jee", "=", "1.1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jei", "=", "0.9"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jie", "=", "2"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jii", "=", "1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"n", "=", "3"}], ";"}], " ", "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"ge", "=", "0.4"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"gi", "=", "0.3"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"te", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ti", "=", "1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"detJ", "=",
RowBox[{
RowBox[{
RowBox[{"-", "Jee"}], "*", "Jii"}], "+",
RowBox[{"Jei", "*", "Jie"}]}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"cplus", "=", " ",
RowBox[{
RowBox[{
RowBox[{"-",
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}], "*", "Jii", "*", "ge"}], "+",
"gi"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
RowBox[{"Characteristic", " ", "function", " ", "for", " ", "detJ"}],
">", "0"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"P", "[", "z_", "]"}], "=",
RowBox[{
RowBox[{"detJ", "*",
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"z", "^", "n"}], ",",
RowBox[{"z", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"z", "\[LessEqual]", "0"}]}], "}"}]}], "}"}], "]"}]}],
"+",
RowBox[{
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jii", "*", "z"}], "+",
"cplus"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"F", "[", "z_", "]"}], "=",
RowBox[{
RowBox[{"Jee", "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"z", "^", "n"}], ",",
RowBox[{"z", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"z", "\[LessEqual]", "0"}]}], "}"}]}], "}"}], "]"}]}],
"-",
RowBox[{"Jei", "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"P", "[", "z", "]"}], ")"}], "^", "n"}], ",",
RowBox[{
RowBox[{"P", "[", "z", "]"}], ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{
RowBox[{"P", "[", "z", "]"}], "\[LessEqual]", "0"}]}], "}"}]}],
"}"}], "]"}]}], "-", "z", "+", "ge"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"plot1", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"P", "[", "z", "]"}], ",",
RowBox[{"{",
RowBox[{"z", ",",
RowBox[{"-", "0.01"}], ",", ".6"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<z\>\"", ",", "\"\<P(z)\>\""}], "}"}]}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"Directive", "[",
RowBox[{"Blue", ",", "Bold", ",",
RowBox[{"FontFamily", "\[Rule]", "\"\<Helvetica\>\""}]}], "]"}]}]}],
RowBox[{"(*",
RowBox[{",",
RowBox[{"Ticks", "\[Rule]", "None"}]}], "*)"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot2", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"F", "[", "z", "]"}], ",",
RowBox[{"{",
RowBox[{"z", ",",
RowBox[{"-", "0.01"}], ",", ".6"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<z\>\"", ",", "\"\<F(z)\>\""}], "}"}]}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"Directive", "[",
RowBox[{"Blue", ",", "Bold", ",",
RowBox[{"FontFamily", "\[Rule]", "\"\<Helvetica\>\""}]}], "]"}]}]}],
RowBox[{"(*",
RowBox[{",",
RowBox[{"Ticks", "\[Rule]", "None"}]}], "*)"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{"GraphicsRow", "[",
RowBox[{"{",
RowBox[{"plot1", ",", "plot2"}], "}"}], "]"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<detJ=\>\"", ",", "detJ"}], "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"z0", "=",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{"P", "[", "z", "]"}], "\[Equal]", "0"}], ",", "z"}], "]"}]}],
";", " ",
RowBox[{"(*",
RowBox[{"Zero", " ", "crossing", " ", "of", " ", "P"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<The zero crossing of P is z0=\>\"", ",", " ",
RowBox[{"z", "/.",
RowBox[{"z0", "[",
RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}]}], " ",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Z", "=",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{"F", "[", "z", "]"}], "\[Equal]", "0"}], ",", "z"}], "]"}]}],
";",
RowBox[{"(*",
RowBox[{"Zero", " ", "crossings", " ", "of", " ", "F"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<The unique zero crossing of F is z1=\>\"", ",", " ",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}]}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"Steady", " ", "states", " ", "in", " ", "the", " ", "phase", " ",
"plane"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re1", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}], " ",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"ri1", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"detJ", "*",
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jii", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}]}], "+", "cplus"}], ")"}],
"^", "n"}]}], ";",
RowBox[{"(*",
RowBox[{"steady", " ", "state"}], "*)"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{
"\"\<The unique steady state of the SSN is re=\>\"", ",", " ", "re1",
",", " ", "\"\<, ri=\>\"", ",", " ", "ri1"}], "]"}]}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"Right", " ", "side", " ", "of", " ", "the", " ", "SSN", " ",
"equations"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "x"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Jee", "*", "x"}], "-",
RowBox[{"Jei", "*", "y"}], "+", "ge"}], ")"}], "^", "n"}], "*",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"Jee", "*", "x"}], "-",
RowBox[{"Jei", "*", "y"}], "+", "ge"}], "]"}]}]}], ")"}], "*",
RowBox[{"te", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Gi", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "y"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Jie", "*", "x"}], "-",
RowBox[{"Jii", "*", "y"}], "+", "gi"}], ")"}], "^", "n"}], "*",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"Jie", "*", "x"}], "-",
RowBox[{"Jii", "*", "y"}], "+", "gi"}], "]"}]}]}], ")"}], "*",
RowBox[{"ti", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Clear", "[",
RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}], ";", " ",
RowBox[{"(*",
RowBox[{
RowBox[{"region", " ", "[",
RowBox[{"a", ",", "b"}], "]"}],
RowBox[{"x", "[",
RowBox[{"c", ",", "d"}], "]"}], " ", "in", " ", "the", " ", "phase",
" ", "plane", " ", "containing", " ", "steady", " ", "states"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"a", "=",
RowBox[{"re1", "-", "2"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"b", "=",
RowBox[{"re1", "+", "1"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"c", "=",
RowBox[{"ri1", "-", "1"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"d", "=",
RowBox[{"ri1", "+", "2"}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot3", "=",
RowBox[{"StreamPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x", ",", "y"}], "]"}], ",",
RowBox[{"Gi", "[",
RowBox[{"x", ",", "y"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "a", ",", "b"}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",", "c", ",", "d"}], "}"}], ",",
RowBox[{"StreamStyle", "\[Rule]", "Black"}], ",",
RowBox[{"StreamScale", "\[Rule]", "0.25"}], ",",
RowBox[{"StreamPoints", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.5", ",", "0.5"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.5", ",", "1.5"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "1"}], ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "0.1"}], ",",
RowBox[{"-", "0.5"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "1"}], ",", "0.25"}], "}"}]}], "}"}]}], ",",
RowBox[{"Epilog", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"PointSize", "[", "0.05", "]"}], ",",
RowBox[{"Point", "[",
RowBox[{
RowBox[{"{",
RowBox[{"{",
RowBox[{"re1", ",", "ri1"}], "}"}], "}"}], ",",
RowBox[{"VertexColors", "\[Rule]",
RowBox[{"{", "Black", "}"}]}]}], "]"}]}], "}"}]}], ",",
RowBox[{"GridLines", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"{",
RowBox[{"re1", ",", "Black"}], "}"}], "}"}], ",",
RowBox[{"{",
RowBox[{"{",
RowBox[{"ri1", ",", "Black"}], "}"}], "}"}]}], "}"}]}], ",",
RowBox[{"FrameTicks", "\[Rule]", "None"}]}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot4", "=",
RowBox[{"ContourPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "0"}], ",",
RowBox[{
RowBox[{"Gi", "[",
RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",",
RowBox[{"a", "-", ".2"}], ",",
RowBox[{"b", "+", ".2"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",",
RowBox[{"c", "-", ".2"}], ",",
RowBox[{"d", "+", ".2"}]}], "}"}], ",",
RowBox[{"ContourStyle", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"Red", ",",
RowBox[{"Thickness", "[", "0.01", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"Blue", ",",
RowBox[{"Thickness", "[", "0.01", "]"}]}], "}"}]}], "}"}]}]}],
"]"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"Show", "[",
RowBox[{"plot3", ",", "plot4"}], "]"}],
"\[IndentingNewLine]"}]}]], "Input",
CellChangeTimes->{{3.669965930887747*^9, 3.669965963034878*^9}, {
3.669967911686942*^9, 3.6699679191481867`*^9}, 3.6699747013188877`*^9,
3.670752870993903*^9, {3.671265838922729*^9, 3.671265947489256*^9}, {
3.6712659929321003`*^9, 3.6712660134255743`*^9}, {3.6712660491008797`*^9,
3.671266093601243*^9}, {3.671266154852158*^9, 3.671266246391962*^9}, {
3.671266385127493*^9, 3.671266398789341*^9}, {3.681838415360907*^9,
3.681838594971818*^9}, {3.681838747880744*^9, 3.681838794535638*^9}, {
3.6818396152251*^9, 3.68183965149369*^9}, {3.6818397660694323`*^9,
3.681839800755595*^9}, {3.681870231723321*^9, 3.681870268348049*^9}, {
3.682230153078004*^9, 3.6822301971492233`*^9}, {3.691128262203121*^9,
3.69112827193295*^9}, {3.6911283237560577`*^9, 3.6911284455921*^9}, {
3.69112848496733*^9, 3.691128578011964*^9}, {3.691128815458748*^9,
3.691128841399782*^9}, {3.691131475876326*^9, 3.6911314768269787`*^9}, {
3.691131870507711*^9, 3.691131888177313*^9}, {3.691131933242436*^9,
3.6911319338471746`*^9}, {3.691132210341564*^9, 3.691132298527499*^9},
3.691132351831217*^9, {3.691315245031262*^9, 3.691315276478383*^9}, {
3.691315628391818*^9, 3.691315708164516*^9}, {3.691318047438306*^9,
3.6913180560287123`*^9}, {3.691318097111951*^9, 3.69131811987887*^9}, {
3.691318162393814*^9, 3.691318241958939*^9}, {3.6913182948486633`*^9,
3.6913183161128187`*^9}, {3.691318357286148*^9, 3.6913184797188063`*^9}, {
3.691417970476659*^9, 3.691417995961779*^9}, {3.691418045551126*^9,
3.6914180977795763`*^9}, {3.691418145338976*^9, 3.6914184094990587`*^9}, {
3.691420317108986*^9, 3.691420319003961*^9}, {3.69142871410492*^9,
3.691428756878338*^9}, {3.691428788732399*^9, 3.69142879352136*^9}, {
3.692691013376927*^9, 3.692691065212077*^9}, {3.692691152615541*^9,
3.6926915899112873`*^9}, {3.692691640206373*^9, 3.6926916705650187`*^9}, {
3.69269170220357*^9, 3.6926918804554234`*^9}, {3.692691919439193*^9,
3.6926919642426863`*^9}, {3.692692142992495*^9, 3.6926921495481358`*^9}, {
3.692692182880225*^9, 3.692692199600362*^9}, {3.6926922943415537`*^9,
3.692692313933724*^9}, 3.6926923584113293`*^9, {3.692692407129314*^9,
3.6926924240393*^9}, {3.692692472360632*^9, 3.6926925436914463`*^9}, {
3.692692577442625*^9, 3.692692600988268*^9}, {3.6926926362513323`*^9,
3.6926926913528214`*^9}, {3.692692856574181*^9, 3.692692892698038*^9}, {
3.692692942468071*^9, 3.692692961291857*^9}, {3.692693183889185*^9,
3.6926931851141443`*^9}, {3.6926932152370462`*^9, 3.692693236248979*^9}, {
3.692693394082568*^9, 3.69269355645205*^9}, {3.692693608075405*^9,
3.692693697569433*^9}, {3.6926937618517447`*^9, 3.692693796741599*^9}, {
3.692693848433611*^9, 3.6926939070487843`*^9}, {3.6926940951038437`*^9,
3.692694260466854*^9}, 3.6926943111296053`*^9, {3.692694343104659*^9,
3.692694388378901*^9}, {3.692694419691263*^9, 3.6926945740361977`*^9}, {
3.692694607333618*^9, 3.692694617750513*^9}, {3.692694749430292*^9,
3.6926947567176237`*^9}, {3.6926948933073387`*^9,
3.6926949268416023`*^9}, {3.6926952409073687`*^9, 3.692695377924794*^9}, {
3.692695423465567*^9, 3.6926954906774597`*^9}, {3.6926955497759533`*^9,
3.692695579494293*^9}, {3.692695668163787*^9, 3.6926956691059732`*^9}, {
3.692695812417848*^9, 3.692695875704959*^9}, {3.692695942894755*^9,
3.69269605369267*^9}, {3.692696120742998*^9, 3.692696129232265*^9}, {
3.6926961616616507`*^9, 3.69269619525965*^9}, 3.693037670779304*^9, {
3.6930377357191143`*^9, 3.693037763251899*^9}, {3.693037801458839*^9,
3.693037927056592*^9}, {3.693040872757523*^9, 3.6930408824382257`*^9}, {
3.693040927991486*^9, 3.693040948538813*^9}, {3.693041042702565*^9,
3.693041060419207*^9}, {3.693041091856914*^9, 3.693041096462126*^9}, {
3.693041153536542*^9, 3.693041172122979*^9}, {3.69304121023347*^9,
3.693041424919629*^9}, {3.693042275068267*^9, 3.6930423868060503`*^9}, {
3.693042438460918*^9, 3.693042438461648*^9}, {3.69304273333215*^9,
3.6930427504579144`*^9}, {3.693044059170693*^9, 3.693044085208392*^9}, {
3.693044120153393*^9, 3.693044209643271*^9}, {3.693044414183062*^9,
3.693044429338566*^9}, {3.693044479089279*^9, 3.693044500338147*^9}, {
3.6930445989846277`*^9, 3.693044621695581*^9}, {3.693044679822979*^9,
3.6930446832462797`*^9}, {3.69304473535187*^9, 3.6930447924539013`*^9}, {
3.693044851145458*^9, 3.693044858688456*^9}, 3.693044987887783*^9, {
3.693045094291526*^9, 3.693045123618059*^9}, 3.693045240423849*^9, {
3.693045417819585*^9, 3.693045423545686*^9}, {3.6930454726948957`*^9,
3.693045473328208*^9}, {3.693300145689186*^9, 3.6933001587564983`*^9}, {
3.693300274196973*^9, 3.693300295266527*^9}, {3.693300364900671*^9,
3.693300372449574*^9}, {3.6933004346780643`*^9, 3.6933004351279507`*^9}, {
3.693300481923752*^9, 3.693300484878624*^9}, 3.693300516030217*^9, {
3.6933005576602592`*^9, 3.693300564611203*^9}, {3.693300954060238*^9,
3.6933009845199423`*^9}, {3.693301065642104*^9, 3.693301087668187*^9}, {
3.693301134268777*^9, 3.693301137940702*^9}, {3.6933016898324347`*^9,
3.693301693877865*^9}, {3.693301820260469*^9, 3.6933018286349907`*^9}, {
3.693553981246297*^9, 3.6935540601096897`*^9}, {3.6935578660234613`*^9,
3.693557885185216*^9}, {3.693557984099605*^9, 3.693557993563349*^9}, {
3.693558099655369*^9, 3.693558121652178*^9}, {3.693558403576603*^9,
3.6935584113664627`*^9}, {3.693558457176978*^9, 3.6935584685505867`*^9}, {
3.693558514699024*^9, 3.693558550858926*^9}, 3.693633800177897*^9, {
3.6936338593125353`*^9, 3.693633947097559*^9}, {3.6936344743320932`*^9,
3.6936346011781054`*^9}, {3.693634642521132*^9, 3.693634698355796*^9}, {
3.693634736007983*^9, 3.693634822649084*^9}, {3.6936348769128113`*^9,
3.693634889424296*^9}, {3.6936349363573217`*^9, 3.6936351977763653`*^9}, {
3.693635235448841*^9, 3.693635267062992*^9}, {3.693635323085497*^9,
3.693635499107008*^9}, {3.693636415238715*^9, 3.693636594938246*^9}, {
3.693636701087446*^9, 3.693636703844235*^9}, {3.693636774624946*^9,
3.6936368544696827`*^9}, {3.69363699186099*^9, 3.693636995395925*^9}, {
3.693637935003998*^9, 3.693637966682323*^9}, {3.693638093613104*^9,
3.693638094085292*^9}, {3.6936396523190937`*^9, 3.693639658103911*^9}, {
3.69363969929668*^9, 3.6936397596283417`*^9}, {3.693639805226301*^9,
3.693639814435791*^9}, {3.693655084684061*^9, 3.69365510405702*^9}, {
3.693656272938631*^9, 3.6936562764852657`*^9}, {3.693657938887617*^9,
3.6936579389870453`*^9}, {3.693660052589501*^9, 3.69366005290396*^9}, {
3.693660103834487*^9, 3.693660104854559*^9}, {3.6992662295311317`*^9,
3.699266282030658*^9}, {3.699266315994287*^9, 3.6992663646020317`*^9}, {
3.699266474635482*^9, 3.699266493432049*^9}, {3.69926683000631*^9,
3.699266858609324*^9}, {3.699267027181714*^9, 3.699267056837557*^9}, {
3.699267088728222*^9, 3.699267094888064*^9}, {3.699267137905382*^9,
3.6992671731307783`*^9}, {3.699267242193976*^9, 3.699267251621809*^9}, {
3.699267656382222*^9, 3.699267734275045*^9}, {3.699268323996841*^9,
3.699268330043393*^9}, {3.699274329243966*^9, 3.699274354521453*^9}, {
3.699274397837099*^9, 3.699274417061928*^9}, {3.699291258653414*^9,
3.699291260810226*^9}, {3.6992937325902863`*^9, 3.699293735169125*^9}, {
3.709996310247995*^9, 3.709996464434144*^9}, {3.709996498535972*^9,
3.7099965081035*^9}, {3.709996553650486*^9, 3.70999657071524*^9}, {
3.7099966430770817`*^9, 3.709996675965165*^9}, {3.709996717796789*^9,
3.709996759978467*^9}, {3.70999679705254*^9, 3.709996803103643*^9}, {
3.709996840150889*^9, 3.7099968909056873`*^9}, {3.709996939976469*^9,
3.7099969687815*^9}, {3.709997015550963*^9, 3.709997057555914*^9}, {
3.709997167162862*^9, 3.709997171108571*^9}, 3.710006716398745*^9, {
3.710821614361597*^9, 3.710821633858446*^9}}],
Cell[BoxData[
GraphicsBox[{{}, {InsetBox[
GraphicsBox[{{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.],
LineBox[{{-0.009999987551020408, -0.15555554172335606`}, \
{-0.00981290207609477, -0.15534766897343869`}, {-0.00962581660116913, \
-0.1551397962235213}, {-0.009251645651317855, -0.15472405072368656`}, \
{-0.008503303751615301, -0.15389255972401705`}, {-0.007006619952210195, \
-0.15222957772467804`}, {-0.004013252353399982, -0.14890361372600003`}, \
{-0.00019451530612244898`, -0.1446605725623583}}], LineBox[CompressedData["
1:eJwVyXs0VAkAx/FpMlsqpVWRtSKnpjJbBmVV+qlFiYoecyw2Sltep+zuoW1a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"]]}, {}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox["\"z\"", TraditionalForm],
FormBox["\"P(z)\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
RGBColor[0, 0, 1], Bold, FontFamily -> "Helvetica"],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{-0.01, 0.6}, {-0.15555554172335606`, 0.69022219793288}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}], {192., -116.80842387373012`},
ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}], InsetBox[
GraphicsBox[{{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.],
LineBox[{{-0.009999987551020408,
0.4099999875510204}, {-0.00981290207609477,
0.4098129020760948}, {-0.00962581660116913,
0.40962581660116915`}, {-0.009251645651317855,
0.4092516456513179}, {-0.008503303751615301,
0.4085033037516153}, {-0.007006619952210195,
0.4070066199522102}, {-0.004013252353399982,
0.4040132523534}, {-0.00019451530612244898`, 0.4001945153061225}}],
LineBox[{{0.001973482844220444, 0.3980265256103735}, {
0.014954096803595674`, 0.3850495817174763}, {0.02707450746454802,
0.3729473235731408}, {0.03895716378126323, 0.3611078723469746}, {
0.05184696366211282, 0.34830634357898715`}, {0.06387656024453953,
0.3364101328610381}, {0.0769133003911006, 0.3235871914796692}, {
0.08971228619342454, 0.31108194777576}, {0.1016510686973256,
0.2995043211098196}, {0.11459699476536103`, 0.28705844114250423`}, {
0.1266827175349736, 0.27555365833862033`}, {0.12831971432882724`,
0.27400448214224793`}}], LineBox[CompressedData["
1:eJwBwQM+/CFib1JlAgAAADsAAAACAAAAOJjYnl+7wT88Jt6gzevQP0sCox2c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"]]}, {}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox["\"z\"", TraditionalForm],
FormBox["\"F(z)\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
RGBColor[0, 0, 1], Bold, FontFamily -> "Helvetica"],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{-0.01, 0.6}, {-0.2583438231069499, 0.4099999875510204}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}], {576., -116.80842387373012`},
ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}]}, {}},
ContentSelectable->True,
PlotRangePadding->{6, 5}]], "Output",
CellChangeTimes->{{3.6930448384819927`*^9, 3.693044859488907*^9},
3.693044989207708*^9, {3.6930451006531467`*^9, 3.693045125232478*^9},
3.693045246281494*^9, 3.6930454250975924`*^9, 3.693045475412416*^9, {
3.693300147021147*^9, 3.693300160029902*^9}, {3.693300279216797*^9,
3.6933003036904097`*^9}, 3.6933003924435387`*^9, {3.693300488788917*^9,
3.6933005170604753`*^9}, 3.693300569042886*^9, 3.693301093693428*^9,
3.693301139126978*^9, 3.693301695456842*^9, {3.6933018222520323`*^9,
3.693301834054962*^9}, 3.6935539528522243`*^9, {3.693553985954308*^9,
3.69355400092*^9}, {3.6935540442505617`*^9, 3.693554061193859*^9},
3.693557849304264*^9, 3.6935578861674347`*^9, 3.693557994602542*^9,
3.6935581225998*^9, 3.693558412595677*^9, 3.6935584693876247`*^9, {
3.693558523527027*^9, 3.6935585515527363`*^9}, 3.693633505977499*^9,
3.693633804846588*^9, {3.693633870555887*^9, 3.6936339182956667`*^9},
3.69363394963232*^9, {3.693634523755886*^9, 3.693634558535604*^9},
3.693634604389668*^9, {3.6936347593721867`*^9, 3.693634806694268*^9}, {
3.693634868254922*^9, 3.693634889920994*^9}, {3.693634939369061*^9,
3.693634964597478*^9}, 3.6936350115683727`*^9, {3.6936351097446003`*^9,
3.6936351362934093`*^9}, 3.6936352032119827`*^9, 3.693635236965022*^9,
3.693635268416267*^9, {3.693635342433133*^9, 3.693635353830261*^9},
3.693635414186887*^9, 3.693635456441825*^9, 3.693636436415922*^9,
3.6936366073125067`*^9, 3.6936367044767303`*^9, {3.6936368271333323`*^9,
3.693636857055181*^9}, 3.693637977870657*^9, 3.6936550858463078`*^9,
3.693655697884179*^9, 3.693656196420047*^9, 3.693656277414295*^9,
3.693659912174467*^9, 3.693660053729073*^9, 3.693660097083301*^9,
3.699266324328162*^9, 3.699266366607069*^9, {3.699266475879183*^9,
3.699266493915804*^9}, 3.699266859783309*^9, {3.699267033924588*^9,
3.699267057407189*^9}, 3.699267097284881*^9, {3.699267139511035*^9,
3.699267174258349*^9}, 3.699267252023003*^9, {3.699267657492249*^9,
3.6992676843445253`*^9}, {3.699267719163569*^9, 3.6992677362075863`*^9},
3.6992683322346*^9, {3.699274349458699*^9, 3.699274354994232*^9}, {
3.699274399119*^9, 3.699274417549514*^9}, 3.699293736530676*^9,
3.70999651270955*^9, 3.709996579066434*^9, {3.7099966518140593`*^9,
3.7099966776651173`*^9}, 3.7099967620962954`*^9, 3.7099968945651217`*^9, {
3.70999701641816*^9, 3.709997058402185*^9}, 3.70999717260888*^9, {
3.710821615826844*^9, 3.7108216383434963`*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"detJ=\"\>", "\[InvisibleSpace]", "0.7`"}],
SequenceForm["detJ=", 0.7],
Editable->False]], "Print",
CellChangeTimes->{{3.693300147037521*^9, 3.693300160049631*^9}, {
3.693300279224373*^9, 3.693300303697177*^9}, 3.693300392448848*^9, {
3.6933004887844257`*^9, 3.693300517054727*^9}, 3.693300568969665*^9,
3.6933010930781517`*^9, 3.693301138834792*^9, 3.693301695107812*^9, {
3.693301822171623*^9, 3.693301833967244*^9}, 3.693553951830721*^9, {
3.693553985720915*^9, 3.693554000865996*^9}, {3.6935540441974487`*^9,
3.693554061139205*^9}, 3.693557849252488*^9, 3.6935578860847387`*^9,
3.693557994530972*^9, 3.693558122534677*^9, 3.693558412405761*^9,
3.693558469175111*^9, {3.693558523463127*^9, 3.693558551490391*^9},
3.693633504911581*^9, 3.693633804732128*^9, {3.6936338704560337`*^9,
3.6936339182227173`*^9}, 3.693633949554431*^9, {3.6936345236484947`*^9,
3.693634558401764*^9}, 3.6936346043127832`*^9, {3.693634759278812*^9,
3.6936348066211977`*^9}, {3.693634868172909*^9, 3.693634889806417*^9}, {
3.693634939289071*^9, 3.693634964525217*^9}, 3.69363501148323*^9, {
3.693635109669422*^9, 3.6936351362146177`*^9}, 3.693635203134584*^9,
3.693635236878072*^9, 3.693635268345574*^9, {3.693635342321246*^9,
3.693635353752825*^9}, 3.69363541410168*^9, 3.69363545632376*^9,
3.6936364363345413`*^9, 3.6936366071994762`*^9, 3.6936367043984127`*^9, {
3.693636827058785*^9, 3.693636856983314*^9}, 3.693637977801016*^9,
3.6936550857709017`*^9, 3.693655697807871*^9, 3.693656196148354*^9,
3.693656277345263*^9, 3.693659911974712*^9, 3.6936600536622133`*^9,
3.693660097014222*^9, 3.699266323576779*^9, 3.699266366533163*^9, {
3.699266475805846*^9, 3.6992664938431807`*^9}, 3.6992668597073393`*^9, {
3.699267033846323*^9, 3.699267057326449*^9}, 3.699267097207287*^9, {
3.6992671394364347`*^9, 3.6992671741847553`*^9}, 3.699267251946439*^9, {
3.699267657414487*^9, 3.69926768427127*^9}, {3.699267719087634*^9,
3.699267736132443*^9}, 3.6992683319989443`*^9, {3.699274349380067*^9,
3.699274354920266*^9}, {3.6992743990399313`*^9, 3.699274417473796*^9},
3.6992937364511757`*^9, 3.709996512496706*^9, 3.7099965789937353`*^9, {
3.709996651742*^9, 3.709996677570758*^9}, 3.70999676201997*^9,
3.709996894585876*^9, {3.709997016434312*^9, 3.70999705842448*^9},
3.709997172626698*^9, {3.710821616101922*^9, 3.710821638363069*^9}}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"The zero crossing of P is z0=\"\>", "\[InvisibleSpace]",
"0.12851422963494974`"}],
SequenceForm["The zero crossing of P is z0=", 0.12851422963494974`],
Editable->False]], "Print",
CellChangeTimes->{{3.693300147037521*^9, 3.693300160049631*^9}, {
3.693300279224373*^9, 3.693300303697177*^9}, 3.693300392448848*^9, {
3.6933004887844257`*^9, 3.693300517054727*^9}, 3.693300568969665*^9,
3.6933010930781517`*^9, 3.693301138834792*^9, 3.693301695107812*^9, {
3.693301822171623*^9, 3.693301833967244*^9}, 3.693553951830721*^9, {
3.693553985720915*^9, 3.693554000865996*^9}, {3.6935540441974487`*^9,
3.693554061139205*^9}, 3.693557849252488*^9, 3.6935578860847387`*^9,
3.693557994530972*^9, 3.693558122534677*^9, 3.693558412405761*^9,
3.693558469175111*^9, {3.693558523463127*^9, 3.693558551490391*^9},
3.693633504911581*^9, 3.693633804732128*^9, {3.6936338704560337`*^9,
3.6936339182227173`*^9}, 3.693633949554431*^9, {3.6936345236484947`*^9,
3.693634558401764*^9}, 3.6936346043127832`*^9, {3.693634759278812*^9,
3.6936348066211977`*^9}, {3.693634868172909*^9, 3.693634889806417*^9}, {
3.693634939289071*^9, 3.693634964525217*^9}, 3.69363501148323*^9, {
3.693635109669422*^9, 3.6936351362146177`*^9}, 3.693635203134584*^9,
3.693635236878072*^9, 3.693635268345574*^9, {3.693635342321246*^9,
3.693635353752825*^9}, 3.69363541410168*^9, 3.69363545632376*^9,
3.6936364363345413`*^9, 3.6936366071994762`*^9, 3.6936367043984127`*^9, {
3.693636827058785*^9, 3.693636856983314*^9}, 3.693637977801016*^9,
3.6936550857709017`*^9, 3.693655697807871*^9, 3.693656196148354*^9,
3.693656277345263*^9, 3.693659911974712*^9, 3.6936600536622133`*^9,
3.693660097014222*^9, 3.699266323576779*^9, 3.699266366533163*^9, {
3.699266475805846*^9, 3.6992664938431807`*^9}, 3.6992668597073393`*^9, {
3.699267033846323*^9, 3.699267057326449*^9}, 3.699267097207287*^9, {
3.6992671394364347`*^9, 3.6992671741847553`*^9}, 3.699267251946439*^9, {
3.699267657414487*^9, 3.69926768427127*^9}, {3.699267719087634*^9,
3.699267736132443*^9}, 3.6992683319989443`*^9, {3.699274349380067*^9,
3.699274354920266*^9}, {3.6992743990399313`*^9, 3.699274417473796*^9},
3.6992937364511757`*^9, 3.709996512496706*^9, 3.7099965789937353`*^9, {
3.709996651742*^9, 3.709996677570758*^9}, 3.70999676201997*^9,
3.709996894585876*^9, {3.709997016434312*^9, 3.70999705842448*^9},
3.709997172626698*^9, {3.710821616101922*^9, 3.710821638368043*^9}}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"The unique zero crossing of F is z1=\"\>", "\[InvisibleSpace]",
"0.43183905443673043`"}],
SequenceForm["The unique zero crossing of F is z1=", 0.43183905443673043`],
Editable->False]], "Print",
CellChangeTimes->{{3.693300147037521*^9, 3.693300160049631*^9}, {
3.693300279224373*^9, 3.693300303697177*^9}, 3.693300392448848*^9, {
3.6933004887844257`*^9, 3.693300517054727*^9}, 3.693300568969665*^9,
3.6933010930781517`*^9, 3.693301138834792*^9, 3.693301695107812*^9, {
3.693301822171623*^9, 3.693301833967244*^9}, 3.693553951830721*^9, {
3.693553985720915*^9, 3.693554000865996*^9}, {3.6935540441974487`*^9,
3.693554061139205*^9}, 3.693557849252488*^9, 3.6935578860847387`*^9,
3.693557994530972*^9, 3.693558122534677*^9, 3.693558412405761*^9,
3.693558469175111*^9, {3.693558523463127*^9, 3.693558551490391*^9},
3.693633504911581*^9, 3.693633804732128*^9, {3.6936338704560337`*^9,
3.6936339182227173`*^9}, 3.693633949554431*^9, {3.6936345236484947`*^9,
3.693634558401764*^9}, 3.6936346043127832`*^9, {3.693634759278812*^9,
3.6936348066211977`*^9}, {3.693634868172909*^9, 3.693634889806417*^9}, {
3.693634939289071*^9, 3.693634964525217*^9}, 3.69363501148323*^9, {
3.693635109669422*^9, 3.6936351362146177`*^9}, 3.693635203134584*^9,
3.693635236878072*^9, 3.693635268345574*^9, {3.693635342321246*^9,
3.693635353752825*^9}, 3.69363541410168*^9, 3.69363545632376*^9,
3.6936364363345413`*^9, 3.6936366071994762`*^9, 3.6936367043984127`*^9, {
3.693636827058785*^9, 3.693636856983314*^9}, 3.693637977801016*^9,
3.6936550857709017`*^9, 3.693655697807871*^9, 3.693656196148354*^9,
3.693656277345263*^9, 3.693659911974712*^9, 3.6936600536622133`*^9,
3.693660097014222*^9, 3.699266323576779*^9, 3.699266366533163*^9, {
3.699266475805846*^9, 3.6992664938431807`*^9}, 3.6992668597073393`*^9, {
3.699267033846323*^9, 3.699267057326449*^9}, 3.699267097207287*^9, {
3.6992671394364347`*^9, 3.6992671741847553`*^9}, 3.699267251946439*^9, {
3.699267657414487*^9, 3.69926768427127*^9}, {3.699267719087634*^9,
3.699267736132443*^9}, 3.6992683319989443`*^9, {3.699274349380067*^9,
3.699274354920266*^9}, {3.6992743990399313`*^9, 3.699274417473796*^9},
3.6992937364511757`*^9, 3.709996512496706*^9, 3.7099965789937353`*^9, {
3.709996651742*^9, 3.709996677570758*^9}, 3.70999676201997*^9,
3.709996894585876*^9, {3.709997016434312*^9, 3.70999705842448*^9},
3.709997172626698*^9, {3.710821616101922*^9, 3.7108216383722353`*^9}}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"The unique steady state of the SSN is re=\"\>",
"\[InvisibleSpace]", "0.08053149265233484`",
"\[InvisibleSpace]", "\<\", ri=\"\>", "\[InvisibleSpace]",
"0.06305065275648662`"}],
SequenceForm[
"The unique steady state of the SSN is re=", 0.08053149265233484, ", ri=",
0.06305065275648662],
Editable->False]], "Print",
CellChangeTimes->{{3.693300147037521*^9, 3.693300160049631*^9}, {
3.693300279224373*^9, 3.693300303697177*^9}, 3.693300392448848*^9, {
3.6933004887844257`*^9, 3.693300517054727*^9}, 3.693300568969665*^9,
3.6933010930781517`*^9, 3.693301138834792*^9, 3.693301695107812*^9, {
3.693301822171623*^9, 3.693301833967244*^9}, 3.693553951830721*^9, {
3.693553985720915*^9, 3.693554000865996*^9}, {3.6935540441974487`*^9,
3.693554061139205*^9}, 3.693557849252488*^9, 3.6935578860847387`*^9,
3.693557994530972*^9, 3.693558122534677*^9, 3.693558412405761*^9,
3.693558469175111*^9, {3.693558523463127*^9, 3.693558551490391*^9},
3.693633504911581*^9, 3.693633804732128*^9, {3.6936338704560337`*^9,
3.6936339182227173`*^9}, 3.693633949554431*^9, {3.6936345236484947`*^9,
3.693634558401764*^9}, 3.6936346043127832`*^9, {3.693634759278812*^9,
3.6936348066211977`*^9}, {3.693634868172909*^9, 3.693634889806417*^9}, {
3.693634939289071*^9, 3.693634964525217*^9}, 3.69363501148323*^9, {
3.693635109669422*^9, 3.6936351362146177`*^9}, 3.693635203134584*^9,
3.693635236878072*^9, 3.693635268345574*^9, {3.693635342321246*^9,
3.693635353752825*^9}, 3.69363541410168*^9, 3.69363545632376*^9,
3.6936364363345413`*^9, 3.6936366071994762`*^9, 3.6936367043984127`*^9, {
3.693636827058785*^9, 3.693636856983314*^9}, 3.693637977801016*^9,
3.6936550857709017`*^9, 3.693655697807871*^9, 3.693656196148354*^9,
3.693656277345263*^9, 3.693659911974712*^9, 3.6936600536622133`*^9,
3.693660097014222*^9, 3.699266323576779*^9, 3.699266366533163*^9, {
3.699266475805846*^9, 3.6992664938431807`*^9}, 3.6992668597073393`*^9, {
3.699267033846323*^9, 3.699267057326449*^9}, 3.699267097207287*^9, {
3.6992671394364347`*^9, 3.6992671741847553`*^9}, 3.699267251946439*^9, {
3.699267657414487*^9, 3.69926768427127*^9}, {3.699267719087634*^9,
3.699267736132443*^9}, 3.6992683319989443`*^9, {3.699274349380067*^9,
3.699274354920266*^9}, {3.6992743990399313`*^9, 3.699274417473796*^9},
3.6992937364511757`*^9, 3.709996512496706*^9, 3.7099965789937353`*^9, {
3.709996651742*^9, 3.709996677570758*^9}, 3.70999676201997*^9,
3.709996894585876*^9, {3.709997016434312*^9, 3.70999705842448*^9},
3.709997172626698*^9, {3.710821616101922*^9, 3.710821638376109*^9}}]
}, Open ]],
Cell[BoxData[
GraphicsBox[{{{}, {
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBQQG+/iFib1JlAgAAABMAAAACAAAAmykMnCS2/r8ll8MO1pbgv9vN/DoH
9v2/wIBVEBAv4L9irdBw4CL9v0tVn18Det+/Xvdjg1BV/L8aVJGU8Jvev2a8
tI47jfu/u0hYnMnD3b8bDcGuhcr6vw5+y1Nw8dy/HvqG/xIN+r/tPsKXxiTc
vwiUBJ3HVPm/LdYTRa5d27946zejh6H4v6eOlzgJnNq/EhEfLjfz9784syRP
ud/Zv2wVuFm6Sfe/to6SZaAo2b8qCQFC9aT2v/truFigdti/6Pz3AswE9r/j
lW0Fm8nXv0IBm7giafW/QFeJSHIh17/ZJuh+3dH0v/D64v4Hfta/TX7dceA+
9L/Py1EFPt/VvzYYea0PsPO/rhStOPZE1b82BblNTyXzv2wgzHUSr9S/eFQK
vFqf8r+MaGk5XR7Uv2TyrBY=
"]]},
{Arrowheads[{{0.0625, 1.}}],
ArrowBox[{{-1.1135338529063592`, -0.3007498062191221}, \
{-1.0699822553777378`, -0.2889880816889314}, {-1.011659105898364, \
-0.2732372301671322}, {-0.9564824163361805, -0.2583362287355975}, \
{-0.9043169619792666, -0.24424852274877762`}, {-0.8550275181156989, \
-0.23093755756112244`}, {-0.8084788600335547, -0.21836677852708197`}, \
{-0.7645357630209125, -0.20649963100110655`}, {-0.7229799943360239, \
-0.19527607426468085`}, {-0.6836235059752584, -0.18464460798945884`}, \
{-0.6463763503338721, -0.17458148811514435`}, {-0.6111485798071203, \
-0.16506297058144143`}, {-0.577850246790258, -0.15606531132805374`}, \
{-0.5463914036785398, -0.14756476629468507`}, {-0.4886323967515585, \
-0.1319600426468204}, {-0.43703542667303064`, -0.11802122199670972`}, \
{-0.39085760230196054`, -0.10555082683023005`}, {-0.35797215844058256`, \
-0.09668336789248022}}]},
{Arrowheads[{{0.03343011260317715, 1.}}], ArrowBox[CompressedData["
1:eJwBcQGO/iFib1JlAgAAABYAAAACAAAAhR/Y43mv079/QOtlmEi1v8n/3CNW
aNG/4KL9bG7Zsr+DSqjU1EDOv26XUEiNb7C/slAMUA6lxr8YGT97vv6ov713
Am3EmcC/Ccue9sb5or8lAsnVWRa8v64Yjk9OfqC/Hr2rfEN4t7+khIyKAn2c
v3aC12LUA6W/3LooIpxSjb8SWwP1thVxv57OdxJr6Fu/OG1MwlDoYL/t7/4f
AOxLvwAAAAAAAAAAAAAAAAAAAABJm1WZDw2DP+GLXHYBh3E/K5dbKsMdkj9I
w1vlXWmBP60bq6/jy6A/1C0141ZAkT8rjrw9mfamP9bjYJcxaZk/EVVyTUvO
qz+8b5E2uW+gP0GFTJyJ5q8/kjF93XkOpD+HYs16YnSxP+ZEeujwFac/mnGJ
zN+Isj+9vaRzk4epPx6A+ChfVrM/uaDBfeKPqz+icl2erd6zP0XKK84fE60/
uJPO5iI2tD/1XvgufiquP4Uir88=
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBYQGe/iFib1JlAgAAABUAAAACAAAAp+GNIQ2vzz8JbI0yffvtv1NArEI3
tc8/ftztDZ747b+LIt/UyjXRP35gYLjwquy/6hK3Q9qE0j9UWPJCV17rv+tW
DQ56x9M/YKZCvAgU6r80VBFUWv3UP/Ys8DI8zei/wArDFXsm1j8b7Pqm8Ynn
v4p6IlPcQtc/1ONiGClK5r9GmNLhX2bYP75lw+09+OS/hQdZwnl82T9bM4Vs
y6zjv0zItfQphdo/qEyolNFn4r+c2uh4cIDbP52xLGZQKeG/cj7yTk1u3D+O
xCTCj+Lfv87z0XbATt0/Pr2yCnB/3b+1+ofwySHeP0FNA6ZBKdu/H1MUvGnn
3j+sdBaUBODYv+MT0UUMod8/pzg9Byml1r/uKQz9DijgP1ueyDEfetS/gQl1
bE964D/SpbgT517Sv6koI3FHx+A/FE8NrYBT0L9JjdMqgyrhP2fdz662Csu/
Rcq1EA==
"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBkQFu/iFib1JlAgAAABgAAAACAAAA/rIcjKCV4T8YFma5s5PEvzohkFhT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"]]},
{Arrowheads[{{0.03724033409039211, 1.}}],
ArrowBox[{{0.38772738897005143`, 0.4553728786155849}, {
0.3767578814740402, 0.44799926487387753`}, {0.34927603298023613`,
0.4265991548463903}, {0.323810229317417, 0.4043282855688273}, {
0.2786924183241936, 0.35964240717361795`}, {0.2407512831532351,
0.31745830674605696`}, {0.2151216172676358, 0.28677142280760803`}, {
0.19300309505967633`, 0.25874651709069835`}, {0.1577592410202682,
0.21074531794092832`}, {0.13216989188982953`, 0.17282801235011355`}, {
0.11267635521905937`, 0.1414579113775171}, {0.09937619566458196,
0.11803367194613516`}, {0.09052501047369221,
0.10081194129097687`}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBQQG+/iFib1JlAgAAABMAAAACAAAAUTEm74AB5j/+pFyzIIEAQDHzb8VO
4OU/ZvYTFDtoAECm8ZsTQVPlP3vqaZ3h/P8/zQX++QbK5D+1CP12Ci//P9Ej
gSVGROQ/urVBOGlm/j/fPxBDpMHjP9BfmGR2ov0/9FmrUiFC4z/wBgH8MeP8
PxRyUlS9xeI/Hqt7/pso/D88iAVIeEziP1pMCGy0cvs/bpzELVLW4T+m6qZE
e8H6P6mujwVLY+E//oVXiPAU+j/tvmbPYvPgP2QeGjcUbfk/cIeo4O934D8o
y/zQ57P4PwAAAAAAAOA/AAAAAAAA+D/LpsQ/UAHfPxh90y/8QPc/mN58OsEK
3j/ypt3rEIj2P8ZklRSiG90/lAtwj7nU9T84+unBLTTcP6p7b1EiJ/U/8bpW
hx4s3D81DIHlFiH1PzBmlg0=
"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBQQG+/iFib1JlAgAAABMAAAACAAAATDgkG8sd2z85KltUWFb0P/YWoRv/
r9o/OdG4VP8D9D9Ww3QsVvXZP4GSV6EAePM/ENntf6E/2T/MYvIfue/yPyFY
DBbhjtg/GUKJ0Chr8j+KQNDuFOPXP2gwHLNP6vE/SpI5Cj081z+4LavHLW3x
P2JNSGhZmtY/Cjo2DsPz8D80kvBWc2PVP+r334mWCvA/maFjJWc81D98xHH9
mlruP5Z7odM0JdM/EPKB2c+37D8kIKph3B3SP4l48KfLLOs/d0EEIcgk0T8Q
aq7LMLfpP7yRNmNiONA/xNisp6FU6D/lIYJQVrHOP6bE6zseBec/Nn5H4EQL
zT+4LWuIpsjlPwAissbOoso/ebfzNCz64z/jKwMv/3HIP130vxq0VOI/pGAk
RdaQxj8dIYc3G+rgP1xAlxw=
"]]},
{Arrowheads[{{0.022726786981903405`, 1.}}],
ArrowBox[{{0.15992635254765952`, 0.4790359317612799}, {
0.14791574455953588`, 0.44247878588685324`}, {0.13603030109500838`,
0.4059874179989831}, {0.1252816399955316, 0.3725973830310747}, {
0.11558046580907018`, 0.34199334411280363`}, {0.09909164717462327,
0.2884505923698436}, {0.08610598319052704, 0.24397383865944208`}, {
0.07610944497378838, 0.20711502788825276`}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}],
ArrowBox[{{-1.9194685073476652`,
1.9194685073476652`}, {-1.917203313343297,
1.917203313343297}, {-1.8931931038279237`,
1.8931931038279237`}, {-1.869462164003648,
1.869462164003648}, {-1.8460104938704718`,
1.8460104938704718`}, {-1.7999449626774136`,
1.7999449626774136`}, {-1.7549965102487493`,
1.7549965102487493`}, {-1.711165136584479,
1.711165136584479}, {-1.6684508416846024`,
1.6684508416846024`}, {-1.6268536255491202`,
1.6268536255491202`}, {-1.5863734881780314`,
1.5863734881780314`}, {-1.5469080120055216`,
1.5469080120055216`}, {-1.5083547794657757`,
1.5083547794657757`}, {-1.4707137905587933`,
1.4707137905587933`}, {-1.4339850452845746`,
1.4339850452845746`}, {-1.3981685436431202`,
1.3981685436431202`}, {-1.3660624214577546`,
1.3660624214577546`}}]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJxTTMoPSmViYGAQBWIQneUTk+jm8nU/lLZf2PUhwmTvl/1Q2n7RTL/bUpZf
9kNp+09b+5X4d3zeD6Xt++9v1hO0+rwfSttXie3+r7D/034obb8taulUO/dP
+6G0vd2aog+Zlz7uh9L2otzKAosTPu6H0vbW5du+vPz4YT+UtldaOPe0RfmH
/VDangEMPuyH0vZeVhmMpRzv90Np+y4P9vZpEu/2Q2l72Q7Oowf13+6H0vY2
+gn/dfze7IfS9kyb+9k5ul/vh9L2D/ussw+eebUfStvfOJSsFSn8aj+Utn/m
x+F6Pu7lfihtL3lrnQjP5Rf7obQ9AEYYqCs=
"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJxTTMoPSmViYGAQAWIQXXwvwvfCkuf7obS91IdSp/C9z/ZDafvasLXbH7c/
3Q+l7TepM9vxJT3ZD6XtdySXX73m/Xg/lLbv4+Kqs3V9tB9K2wfeCLfe6vNw
P5S2l+z8K7Ax4cF+KG1/0fLb30Sm+/uhtH2N+kKurJi7+6G0/TlttnncL2/t
h9L2SzPCDY3X3tgPpe3LnItqpy68th9K2y9RNLF+vu/KfihtbxW18Iw+0+X9
UNre51zal3dZF/dDafstKXt/SL8+vx9K258uPRbzxubsfihtv6Bu3cOythP7
a8SNza61nbBn2Zd268We4/szdstpTtl73B4AAeCrOg==
"]]},
{Arrowheads[{{0.009695715500715546, 1.}}],
ArrowBox[{{-0.14849590279133124`,
0.14864234452718594`}, {-0.13471453584919546`,
0.1349619109620927}, {-0.11252171872909364`,
0.11330970684327654`}, {-0.08363507495877412,
0.08623682860376655}, {-0.05983858401829984, 0.06575509423735958}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBcQGO/iFib1JlAgAAABYAAAACAAAApuLTWyxM3b8JbI0yffvtv6x1YpQt
Ed2/fL02eBna7b9BSGFI12jbvyQ4gZEg6ey//ikHuN/L2b/8mKuzx/3rv+Ma
VONGOti/+9+13g4Y67/tGkjKDLTWvyYNoBL2N+q/Ri8nlPOi1L+MN8neAwXp
v1B3FnDWpdK/kwARjZ3Y578Q8xVetbzQvzxodx3Dsua/BkVLvCDPzb+GbvyP
dJPlv1ULi+DOTMq/chOg5LF65L8MOesodfLGv/5WYht7aOO/Ks5rlRPAw78s
OUM00Fziv7HKDCaqtcC/+7lCL7FX4b+C9htx43C9vzWRY5yRquC/mpmZmZmZ
ub8AAAAAAADgv87hPcsGArO/dlab/OKR3b+mb3+0/82pvyBG3o9NOdu/DK+P
H9chnL/3ZSPJzevYv5S4zSxXLnq/JuZsTnm01r9b5FfE8GmKP5nSSSFXlNS/
60TEmXRhkD9EO2MBiDjUv9MSxAs=
"]]},
{Arrowheads[{{0.028101667199257795`, 1.}}],
ArrowBox[{{0.04083570856793907, -0.27006983040084986`}, {
0.04633739299126899, -0.2596077980503966}, {
0.06063680744860452, -0.23095458506152408`}, {
0.07973523340976461, -0.19008225519495675`}, {
0.09563626213008278, -0.1528997035820348}, {
0.10866540124838939`, -0.11932139570981762`}, {
0.11914815840351485`, -0.08926179706536438}, {
0.13370608357432767`, -0.03893543509688979}, {0.1428455725010927,
0.007954549781194392}, {0.14510413286021145`, 0.04054356519161871}, {
0.14309505404248968`, 0.06226469325436472}}]}},
{GrayLevel[0],
{Arrowheads[{{0.06250000000000001, 1.}}], ArrowBox[CompressedData["
1:eJxTTMoPSmViYGAQAWIQPVuTZ47Ktn/7IfQ9+4wJGS0JUf/2Q+h79i+vnUpx
afu7H0LftT/e/5nz1fY/+yH0HXvG3Y+KA9//3g+hb9tPi5ixqErn934Ifdu+
I0NkWmr+r/0Q+pZ9fr/p8frtP/dD6Jv2TwtvrTNj+bkfQt+0f83P7NsV+mM/
hL5hX5O5fmHV6u/7IfR1+3l199ews33fD6Gv2wf4T84zTP22H0Jfs59w+9Sz
7ye+7ofQV+3jlNtEow2/7ofQV+0XnbDneTb3y34IfcXeObfojjLfl/0Q+oq9
o6Bcm0jT5/0Q+rL97C1OnDt+ftoPoS/ZH5Xxnaw/4dN+CH3JHgC4qavy
"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJxTTMoPSmViYGAQBmIQzWMn9/PWgY/7IfRF+yXW/VOc/n7YD6Ev2IeX/Zfe
XfNhP4S+YM8ABh/2Q+gL9i27LbnuSb7bD6HP2Ze+D5OaGvBmP4Q+Y7947fvv
T6a82g+hT9kHNNQXpH15sR9Cn7CXqF8rW5r7fD+EPm4/9aDCzJx/T/dD6KP2
Z+5Zb3qw9Ml+CH3Efn9uokVq0uP9EPqwvQ17ic32nQ/3Q+iD9vc2haudMnuw
H0IfsO99wavZt+rufgi911533g+vdYq390Po3fYVK9b8LTt3Y38G39TfZed2
2C9ovKl2ft21/XVcnrLn122zPzRH69D07Gv7Z7nN3zY9e5s9AOtQo+M=
"]]},
{Arrowheads[{{0.012911112156425845`, 1.}}],
ArrowBox[{{-0.2996991531886695,
0.07492477784368375}, {-0.29625378467539437`,
0.0740634350345172}, {-0.24746272393460259`,
0.06187804531309722}, {-0.20658967245132,
0.05170932772128085}, {-0.1721222424078888,
0.04321617948068926}, {-0.14274939726869576`,
0.03612624156157791}}]}}}}, GraphicsComplexBox[CompressedData["
1:eJxF13c81f////GTt1EZlVHRUCka3pLISO+71VSIimjQQCHjLU1KpBLKaNiy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"], {{}, {},
TagBox[
TooltipBox[
{RGBColor[1, 0, 0], Thickness[0.01],
LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51,
52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68,
69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85,
86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101,
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115,
116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128,
129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139}],
LineBox[{140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151,
152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165,
166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178,
179, 180, 181, 182, 183, 184, 185, 186, 187, 188}]},
RowBox[{
RowBox[{
RowBox[{"-", "x"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"0.4`", "\[VeryThinSpace]"}], "+",
RowBox[{"1.1`", " ", "x"}], "-",
RowBox[{"0.9`", " ", "y"}]}], ")"}], "3"], " ",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"0.4`", "\[VeryThinSpace]"}], "+",
RowBox[{"1.1`", " ", "x"}], "-",
RowBox[{"0.9`", " ", "y"}]}], "]"}]}]}], "\[Equal]", "0"}]],
Annotation[#, -$CellContext`x + (0.4 + 1.1 $CellContext`x -
0.9 $CellContext`y)^3
HeavisideTheta[0.4 + 1.1 $CellContext`x - 0.9 $CellContext`y] == 0,
"Tooltip"]& ],
TagBox[
TooltipBox[
{RGBColor[0, 0, 1], Thickness[0.01], LineBox[CompressedData["
1:eJwN0NdCDQAAANBbKFFCCEmSJNEWUiqhTW7rvQ/gg/qWpL2s0tIgkYhK0bbO
w/mBk9j8JPg4JBAItNDKU9p4RjsddNJFNz300kc/AwzynBe85BWvGWKYN4ww
yhjjTPCWSaaYZoZ3vGeWD8zxkU/M85kFvvCVRb7xnSWWWeEHq6zxk1+ss8Em
W2yzwy6/+cNf/hGQEkIoe9jLPsIIZz8RHOAgkURxiGgOc4SjxHCM45wglpOc
4jRxnCGesyRwjkTOk8QFkrlICpdI5TJpXOEq6WSQSRbZ5JDLNfK4zg1uks8t
CijkNkUUU8IdSrnLPe5TRjkVVFJFNTU84CG1PCJIHfU00EgT/wEYZ0u1
"]],
LineBox[{344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355,
356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369,
370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382,
383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396,
397, 398, 399}]},
RowBox[{
RowBox[{
RowBox[{"-", "y"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"0.3`", "\[VeryThinSpace]"}], "+",
RowBox[{"2", " ", "x"}], "-", "y"}], ")"}], "3"], " ",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"0.3`", "\[VeryThinSpace]"}], "+",
RowBox[{"2", " ", "x"}], "-", "y"}], "]"}]}]}], "\[Equal]",
"0"}]],
Annotation[#, -$CellContext`y + (0.3 +
2 $CellContext`x - $CellContext`y)^3
HeavisideTheta[0.3 + 2 $CellContext`x - $CellContext`y] == 0,
"Tooltip"]& ]}]},
AspectRatio->1,
DisplayFunction->Identity,
Epilog->{
PointSize[0.05],
PointBox[{{0.08053149265233484, 0.06305065275648662}}, VertexColors -> {
GrayLevel[0]}]},
Frame->True,
FrameTicks->{{None, None}, {None, None}},
GridLines->{{{0.08053149265233484,
GrayLevel[0]}}, {{0.06305065275648662,
GrayLevel[0]}}},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
Method->{
"DefaultBoundaryStyle" -> Automatic, "TransparentPolygonMesh" -> True},
PlotRange->{{-1.9847372916783081`,
1.1458002769829778`}, {-1.0022181315741565`, 2.12831943708713}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.05],
Scaled[0.05]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.6930448384819927`*^9, 3.693044859488907*^9},
3.693044989207708*^9, {3.6930451006531467`*^9, 3.693045125232478*^9},
3.693045246281494*^9, 3.6930454250975924`*^9, 3.693045475412416*^9, {
3.693300147021147*^9, 3.693300160029902*^9}, {3.693300279216797*^9,
3.6933003036904097`*^9}, 3.6933003924435387`*^9, {3.693300488788917*^9,
3.6933005170604753`*^9}, 3.693300569042886*^9, 3.693301093693428*^9,
3.693301139126978*^9, 3.693301695456842*^9, {3.6933018222520323`*^9,
3.693301834054962*^9}, 3.6935539528522243`*^9, {3.693553985954308*^9,
3.69355400092*^9}, {3.6935540442505617`*^9, 3.693554061193859*^9},
3.693557849304264*^9, 3.6935578861674347`*^9, 3.693557994602542*^9,
3.6935581225998*^9, 3.693558412595677*^9, 3.6935584693876247`*^9, {
3.693558523527027*^9, 3.6935585515527363`*^9}, 3.693633505977499*^9,
3.693633804846588*^9, {3.693633870555887*^9, 3.6936339182956667`*^9},
3.69363394963232*^9, {3.693634523755886*^9, 3.693634558535604*^9},
3.693634604389668*^9, {3.6936347593721867`*^9, 3.693634806694268*^9}, {
3.693634868254922*^9, 3.693634889920994*^9}, {3.693634939369061*^9,
3.693634964597478*^9}, 3.6936350115683727`*^9, {3.6936351097446003`*^9,
3.6936351362934093`*^9}, 3.6936352032119827`*^9, 3.693635236965022*^9,
3.693635268416267*^9, {3.693635342433133*^9, 3.693635353830261*^9},
3.693635414186887*^9, 3.693635456441825*^9, 3.693636436415922*^9,
3.6936366073125067`*^9, 3.6936367044767303`*^9, {3.6936368271333323`*^9,
3.693636857055181*^9}, 3.693637977870657*^9, 3.6936550858463078`*^9,
3.693655697884179*^9, 3.693656196420047*^9, 3.693656277414295*^9,
3.693659912174467*^9, 3.693660053729073*^9, 3.693660097083301*^9,
3.699266324328162*^9, 3.699266366607069*^9, {3.699266475879183*^9,
3.699266493915804*^9}, 3.699266859783309*^9, {3.699267033924588*^9,
3.699267057407189*^9}, 3.699267097284881*^9, {3.699267139511035*^9,
3.699267174258349*^9}, 3.699267252023003*^9, {3.699267657492249*^9,
3.6992676843445253`*^9}, {3.699267719163569*^9, 3.6992677362075863`*^9},
3.6992683322346*^9, {3.699274349458699*^9, 3.699274354994232*^9}, {
3.699274399119*^9, 3.699274417549514*^9}, 3.699293736530676*^9,
3.70999651270955*^9, 3.709996579066434*^9, {3.7099966518140593`*^9,
3.7099966776651173`*^9}, 3.7099967620962954`*^9, 3.7099968945651217`*^9, {
3.70999701641816*^9, 3.709997058402185*^9}, 3.70999717260888*^9, {
3.710821615826844*^9, 3.710821638651218*^9}}]
}, Open ]],
Cell[BoxData[""], "Input",
CellChangeTimes->{3.6930449731364183`*^9, 3.693300228310754*^9}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{"Figure", " ", "2",
RowBox[{"(", "B", ")"}]}], ",", " ",
RowBox[{"two", " ", "steady", " ", "states"}]}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Clear", "[",
RowBox[{
"Jee", ",", "Jei", ",", "Jie", ",", "Jii", ",", "ge", ",", "gi", ",", "n",
",", "te", ",", "ti", ",", "cminus", ",", "F", ",", "P", ",", "Z", ",",
"z0", ",", "re1", ",", "ri1", ",", "re2", ",", "ri2", ",", "plot1", ",",
"plot2", ",", "plot3", ",", "plot4", ",", "Ge", ",", "Gi"}], "]"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{"**", "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "********)"}],
"\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{"SSN", " ", "parameters"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**"}], "********)"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Jee", "=", "1.5"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jei", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jie", "=", "0.5"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jii", "=", "1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"n", "=", "3"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"ge", "=", "0.1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"gi", "=", "0.1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"te", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ti", "=", "1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"detJ", "=",
RowBox[{
RowBox[{
RowBox[{"-", "Jee"}], "*", "Jii"}], "+",
RowBox[{"Jei", "*", "Jie"}]}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"cminus", "=",
RowBox[{
RowBox[{
RowBox[{"-",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}], "*", "Jee", "*", "gi"}], "+",
"ge"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
RowBox[{"Characteristic", " ", "function", " ", "for", " ", "detJ"}],
"<", "0"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"P", "[", "z_", "]"}], "=",
RowBox[{
RowBox[{
RowBox[{"-", "detJ"}], "*",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"z", "^", "n"}], ",",
RowBox[{"z", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"z", "\[LessEqual]", "0"}]}], "}"}]}], "}"}], "]"}]}],
"+",
RowBox[{
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jee", "*", "z"}], "+",
"cminus"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"F", "[", "z_", "]"}], "=",
RowBox[{
RowBox[{"Jie", "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"P", "[", "z", "]"}], ")"}], "^", "n"}], ",",
RowBox[{
RowBox[{"P", "[", "z", "]"}], ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{
RowBox[{"P", "[", "z", "]"}], "\[LessEqual]", "0"}]}], "}"}]}],
"}"}], "]"}]}], "-",
RowBox[{"Jii", "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"z", "^", "n"}], ",",
RowBox[{"z", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"z", "\[LessEqual]", "0"}]}], "}"}]}], "}"}], "]"}]}],
"-", "z", "+", "gi"}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"plot1", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"P", "[", "z", "]"}], ",",
RowBox[{"{",
RowBox[{"z", ",",
RowBox[{"-", "0.01"}], ",", ".2"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<z\>\"", ",", "\"\<P(z)\>\""}], "}"}]}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"Directive", "[",
RowBox[{"Blue", ",", "Bold", ",",
RowBox[{"FontFamily", "\[Rule]", "\"\<Helvetica\>\""}]}], "]"}]}]}],
RowBox[{"(*",
RowBox[{",",
RowBox[{"Ticks", "\[Rule]", "None"}]}], "*)"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot2", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"F", "[", "z", "]"}], ",",
RowBox[{"{",
RowBox[{"z", ",",
RowBox[{"-", "0.01"}], ",", ".34"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<z\>\"", ",", "\"\<F(z)\>\""}], "}"}]}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"Directive", "[",
RowBox[{"Blue", ",", "Bold", ",",
RowBox[{"FontFamily", "\[Rule]", "\"\<Helvetica\>\""}]}], "]"}]}]}],
RowBox[{"(*",
RowBox[{",",
RowBox[{"Ticks", "\[Rule]", "None"}]}], "*)"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{"GraphicsRow", "[",
RowBox[{"{",
RowBox[{"plot1", ",", "plot2"}], "}"}], "]"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<detJ=\>\"", ",", "detJ"}], "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"z0", "=",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{"P", "[", "z", "]"}], "\[Equal]", "0"}], ",", "z"}], "]"}]}],
";"}],
RowBox[{"(*",
RowBox[{"Zero", " ", "crossing", " ", "of", " ", "P"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<The zero crossing of P is z0=\>\"", ",", " ",
RowBox[{"z", "/.",
RowBox[{"z0", "[",
RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Z", "=",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{"F", "[", "z", "]"}], "\[Equal]", "0"}], ",", "z"}], "]"}]}],
";"}],
RowBox[{"(*",
RowBox[{"Zero", " ", "crossings", " ", "of", " ", "F"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<Two zero crossings of F are z1=\>\"", ",", " ",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ",", "\"\<, z2=\>\"", ",",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}]}], "]"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"Two", " ", "steady", " ", "states", " ", "in", " ", "the", " ", "phase",
" ", "plane"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re1", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "detJ"}], "*",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jee", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}]}], "+", "cminus"}], ")"}],
"^", "n"}]}], ";"}], " ",
RowBox[{"(*",
RowBox[{"steady", " ", "states"}], "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ri1", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re2", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "detJ"}], "*",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jee", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}]}], "+", "cminus"}], ")"}],
"^", "n"}]}], ";"}], " ", "\[IndentingNewLine]",
RowBox[{
RowBox[{"ri2", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{
"\"\<Two steady states of the SSN are re1=\>\"", ",", " ", "re1", ",",
" ", "\"\<, ri1=\>\"", ",", " ", "ri1", ",", "\"\< and re2=\>\"", ",",
" ", "re2", ",", " ", "\"\<, ri2=\>\"", ",", " ", "ri2"}], "]"}],
"\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"Right", " ", "hand", " ", "side", " ", "of", " ", "the", " ", "SSN", " ",
"equations"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "x"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Jee", "*", "x"}], "-",
RowBox[{"Jei", "*", "y"}], "+", "ge"}], ")"}], "^", "n"}], "*",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"Jee", "*", "x"}], "-",
RowBox[{"Jei", "*", "y"}], "+", "ge"}], "]"}]}]}], ")"}], "*",
RowBox[{"te", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Gi", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "y"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Jie", "*", "x"}], "-",
RowBox[{"Jii", "*", "y"}], "+", "gi"}], ")"}], "^", "n"}], "*",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"Jie", "*", "x"}], "-",
RowBox[{"Jii", "*", "y"}], "+", "gi"}], "]"}]}]}], ")"}], "*",
RowBox[{"ti", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"Clear", "[",
RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}], " ",
RowBox[{"(*",
RowBox[{
"Define", " ", "the", " ", "plot", " ", "region", " ", "around", " ",
"the", " ", "steady", " ", "states"}], "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"a", "=",
RowBox[{"re1", "-", ".15"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"b", "=",
RowBox[{"re2", "+", ".15"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"c", "=",
RowBox[{"ri1", "-", ".1"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"d", "=",
RowBox[{"ri2", "+", ".2"}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot3", "=",
RowBox[{"StreamPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x", ",", "y"}], "]"}], ",",
RowBox[{"Gi", "[",
RowBox[{"x", ",", "y"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "a", ",", "b"}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",", "c", ",", "d"}], "}"}], ",",
RowBox[{"StreamStyle", "\[Rule]", "Black"}], ",",
RowBox[{"StreamScale", "\[Rule]", "0.25"}], ",",
RowBox[{"(*",
RowBox[{
RowBox[{"StreamPoints", "\[Rule]", "10"}], ","}], "*)"}],
RowBox[{"StreamPoints", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0.2", ",",
RowBox[{"-", "0.01"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.05", ",",
RowBox[{"-", "0.03"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "0.1"}], ",",
RowBox[{"-", "0.05"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "0.1"}], ",", "0.05"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0.1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.2", ",", "0.1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.6", ",", "0.2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.55", ",", "0.2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.5", ",",
RowBox[{"-", "0.03"}]}], "}"}]}], "}"}]}], ",",
RowBox[{"Epilog", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"PointSize", "[", "0.05", "]"}], ",",
RowBox[{"Point", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"re1", ",", "ri1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re2", ",", "ri2"}], "}"}]}], "}"}], ",",
RowBox[{"VertexColors", "\[Rule]",
RowBox[{"{",
RowBox[{"Black", ",", "Blue"}], "}"}]}]}], "]"}]}], "}"}]}],
",",
RowBox[{"GridLines", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"re1", ",", "Black"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re2", ",", "Blue"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"ri1", ",", "Black"}], "}"}], ",",
RowBox[{"{",
RowBox[{"ri2", ",", "Blue"}], "}"}]}], "}"}]}], "}"}]}], ",",
RowBox[{"FrameTicks", "\[Rule]", "None"}]}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot4", "=",
RowBox[{"ContourPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "0"}], ",",
RowBox[{
RowBox[{"Gi", "[",
RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",",
RowBox[{"a", "-", ".1"}], ",",
RowBox[{"b", "+", ".05"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",",
RowBox[{"c", "-", ".03"}], ",",
RowBox[{"d", "+", ".025"}]}], "}"}], ",",
RowBox[{"ContourStyle", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"(*",
RowBox[{"Dashed", ","}], "*)"}],
RowBox[{"Red", ",",
RowBox[{"Thickness", "[", "0.01", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"Blue", ",",
RowBox[{"(*",
RowBox[{"Dashed", ","}], "*)"}],
RowBox[{"Thickness", "[", "0.01", "]"}]}], "}"}]}], "}"}]}]}],
"]"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"Show", "[",
RowBox[{"plot3", ",", "plot4"}], "]"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
]}]}]], "Input",
CellChangeTimes->{{3.669976760285296*^9, 3.6699767697071447`*^9}, {
3.669976808950033*^9, 3.669976810283415*^9}, {3.669976867469818*^9,
3.669976895472739*^9}, 3.670752963405788*^9, {3.67109345022956*^9,
3.6710935092857656`*^9}, {3.671192725139305*^9, 3.671192725545566*^9}, {
3.671192820480826*^9, 3.67119283677774*^9}, {3.673068244969331*^9,
3.673068355055131*^9}, {3.673068570697871*^9, 3.673068630528471*^9}, {
3.673068670808959*^9, 3.673068765238462*^9}, {3.673068802295498*^9,
3.67306880275819*^9}, {3.673069002708515*^9, 3.673069164269264*^9}, {
3.673091525815743*^9, 3.673091603159417*^9}, {3.673091635192567*^9,
3.673091682000566*^9}, {3.673091723445589*^9, 3.673091739810832*^9}, {
3.673091776490674*^9, 3.673091776584593*^9}, {3.6730918143217783`*^9,
3.673091825727133*^9}, {3.673091870794931*^9, 3.6730918717363873`*^9}, {
3.6730924127599277`*^9, 3.673092413900115*^9}, {3.6730924717944098`*^9,
3.6730924724254923`*^9}, {3.682230350646763*^9, 3.682230363249546*^9}, {
3.68223039823943*^9, 3.6822304000612507`*^9}, {3.682230450190497*^9,
3.682230450548172*^9}, {3.6822306503588123`*^9, 3.682230660152068*^9}, {
3.6822307312577477`*^9, 3.682230734944474*^9}, {3.682230778755001*^9,
3.6822307801220217`*^9}, {3.6822308706219177`*^9,
3.6822309054573793`*^9}, {3.682230938119789*^9, 3.682230971292965*^9}, {
3.682231013952443*^9, 3.682231225540408*^9}, {3.682231264098337*^9,
3.682231335691848*^9}, {3.682231368065033*^9, 3.682231408589608*^9}, {
3.682231543383738*^9, 3.682231589365896*^9}, {3.691131494919363*^9,
3.69113159922771*^9}, {3.691131643653534*^9, 3.6911316501668787`*^9}, {
3.69113179217253*^9, 3.6911318608156223`*^9}, {3.691131919083111*^9,
3.6911319207421637`*^9}, {3.6911321471521797`*^9,
3.6911321544813128`*^9}, {3.6911323296274776`*^9, 3.691132340955052*^9}, {
3.6911323741012573`*^9, 3.691132393791033*^9}, {3.691132460927519*^9,
3.691132527875847*^9}, {3.691132564566925*^9, 3.6911325944781237`*^9}, {
3.69113265227317*^9, 3.6911329399129753`*^9}, {3.691132986878059*^9,
3.691133021713471*^9}, {3.691133055389436*^9, 3.6911330579865313`*^9}, {
3.6911330926558037`*^9, 3.6911331240414658`*^9}, 3.691133214595914*^9, {
3.691133245550514*^9, 3.691133470108676*^9}, {3.691133563871346*^9,
3.691133623956128*^9}, {3.691133654703555*^9, 3.691133684237121*^9}, {
3.691133726046979*^9, 3.69113390219396*^9}, {3.691133955389489*^9,
3.6911340003416653`*^9}, {3.691318511198587*^9, 3.69131868026756*^9}, {
3.691318713405282*^9, 3.691318725331513*^9}, 3.691318766153832*^9,
3.691318851825436*^9, {3.69132197320399*^9, 3.691321977774823*^9}, {
3.691322019145131*^9, 3.691322040102771*^9}, {3.691322079033895*^9,
3.691322110642815*^9}, {3.691322149069849*^9, 3.691322445235592*^9}, {
3.691322616316637*^9, 3.691322620456044*^9}, {3.693636906483836*^9,
3.693636924832308*^9}, {3.693636958802606*^9, 3.6936369868778143`*^9}, {
3.693637394866794*^9, 3.693637405596044*^9}, {3.693637438770698*^9,
3.69363747111994*^9}, 3.693637521674704*^9, {3.693637611393464*^9,
3.693637705076434*^9}, {3.693637760749894*^9, 3.693637851855163*^9}, {
3.6936379085314817`*^9, 3.6936379195929832`*^9}, {3.693638001689996*^9,
3.693638068630807*^9}, {3.693638134580224*^9, 3.693638265489361*^9}, {
3.693638318345726*^9, 3.693638322680991*^9}, {3.6936383630256042`*^9,
3.693638451388122*^9}, {3.693638484580824*^9, 3.6936385152055187`*^9}, {
3.693639579577705*^9, 3.693639630436178*^9}, 3.693639686211198*^9, {
3.693639771756015*^9, 3.693639781062119*^9}, {3.693639826556299*^9,
3.693639829308064*^9}, {3.693639911623126*^9, 3.6936399747953672`*^9}, {
3.693656047518086*^9, 3.693656056273081*^9}, {3.6936561058185663`*^9,
3.693656106056384*^9}, {3.693656154573308*^9, 3.693656175606654*^9}, {
3.6936562265781927`*^9, 3.693656229072751*^9}, 3.693656301262835*^9, {
3.6936579456117353`*^9, 3.693657945678184*^9}, {3.693660044206531*^9,
3.693660044595935*^9}, {3.6936601168339767`*^9, 3.69366011792015*^9}, {
3.699291224493331*^9, 3.699291251560835*^9}, {3.699291292865603*^9,
3.699291304389091*^9}, {3.699291473665606*^9, 3.699291613442092*^9}, {
3.699293746868219*^9, 3.699293749399317*^9}, {3.709997089880377*^9,
3.7099971564234962`*^9}}],
Cell[BoxData[
GraphicsBox[{{}, {InsetBox[
GraphicsBox[{{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.],
LineBox[{{-0.009999995714285715, -0.2299999871428572}, \
{-0.009935589239311315, -0.22980676771793399`}, {-0.009871182764336916, \
-0.22961354829301078`}, {-0.009742369814388115, -0.22922710944316438`}, \
{-0.009484743914490515, -0.22845423174347157`}, {-0.008969492114695315, \
-0.22690847634408598`}, {-0.007938988515104913, -0.22381696554531477`}, \
{-0.00587798131592411, -0.21763394394777236`}, {-0.0014092453626965702`, \
-0.20422773608808975`}, {-0.00006696428571428572, -0.2002008928571429}}],
LineBox[CompressedData["
1:eJwVxX0wlHkAB3CV22K74kinF0WZbTuEiUuYr16pROyIdCLFdesl2jjy2omo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"]]}, {}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox["\"z\"", TraditionalForm],
FormBox["\"P(z)\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
RGBColor[0, 0, 1], Bold, FontFamily -> "Helvetica"],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{-0.01, 0.2}, {-0.2299999871428572, 0.41599998611428574`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}], {192., -116.80842387373012`},
ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}], InsetBox[
GraphicsBox[{{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.],
LineBox[{{-0.009999992857142858,
0.10999999285714286`}, {-0.009892648732185524,
0.10989264873218553`}, {-0.00978530460722819,
0.1097853046072282}, {-0.009570616357313523,
0.10957061635731352`}, {-0.00914123985748419,
0.1091412398574842}, {-0.008282486857825521,
0.10828248685782553`}, {-0.006564980858508186,
0.10656498085850818`}, {-0.0031299688598735143`,
0.10312996885987352`}, {-0.00011160714285714287`,
0.10011160714285715`}}],
LineBox[{{0.004317924395505718, 0.09568199509907775}, {
0.011272258381298049`, 0.08872630932261583}, {0.018090175940069075`,
0.08190390396907209}, {0.02548596275694999, 0.07449748323613078}, {
0.032388190304244, 0.06757783465023992}, {0.039868287109647904`,
0.06006834303271653}, {0.0472119674880305, 0.05268279845874213}, {
0.05406208859682619, 0.04577990362738043}, {0.06149007896373177,
0.038277425214627715`}, {0.06635926395818997,
0.033348519578056846`}}], LineBox[CompressedData["
1:eJwV1ns8VNsXAHCPCiGiJIRIeih0I0ktr6K4KqkQJT1uFHkUkkpehUJSEnkL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"]]}, {}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox["\"z\"", TraditionalForm],
FormBox["\"F(z)\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
RGBColor[0, 0, 1], Bold, FontFamily -> "Helvetica"],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{-0.01, 0.34}, {-0.07490300138192721, 0.10999999285714286`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}], {576., -116.80842387373012`},
ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}]}, {}},
ContentSelectable->True,
PlotRangePadding->{6, 5}]], "Output",
CellChangeTimes->{{3.6699768032594643`*^9, 3.669976811777919*^9}, {
3.6699768718509502`*^9, 3.6699768979311953`*^9}, {3.671093452586643*^9,
3.6710935102663813`*^9}, {3.6711927175580587`*^9, 3.671192727770483*^9}, {
3.671192822041162*^9, 3.6711928386814823`*^9}, {3.673068247131949*^9,
3.673068356813676*^9}, 3.673068597293851*^9, 3.67306863268204*^9, {
3.673068673506373*^9, 3.6730687676141567`*^9}, 3.673068804911664*^9, {
3.673069006639491*^9, 3.673069116608088*^9}, 3.673069149271153*^9,
3.673091493191065*^9, 3.6730917428665037`*^9, 3.673091777141881*^9,
3.673091827941276*^9, 3.6730918727287903`*^9, 3.673092416709937*^9,
3.6730924734290743`*^9, {3.682230352723344*^9, 3.682230364360816*^9},
3.6822304016284237`*^9, 3.682230452079362*^9, 3.68223067486692*^9,
3.682230741442252*^9, 3.68223078479597*^9, 3.682230913608121*^9, {
3.682230949853684*^9, 3.6822309720720263`*^9}, {3.682231015561976*^9,
3.682231226074185*^9}, {3.682231265091152*^9, 3.682231336632937*^9}, {
3.682231393766885*^9, 3.68223140917111*^9}, {3.682231562412106*^9,
3.682231590222247*^9}, 3.6911316002285423`*^9, 3.6911316518605947`*^9,
3.691131837898481*^9, 3.69113197292867*^9, 3.691132192737213*^9, {
3.69113233006488*^9, 3.6911323414242353`*^9}, 3.691132400528872*^9,
3.6911324624080343`*^9, {3.6911325007837067`*^9, 3.691132528614489*^9},
3.691132565100687*^9, 3.691132595515601*^9, 3.69113271312779*^9,
3.691132791145338*^9, {3.691132930436285*^9, 3.691132940427868*^9}, {
3.6911329992188873`*^9, 3.691133022414216*^9}, 3.691133059462538*^9,
3.691133096502254*^9, 3.691133128741259*^9, 3.691133366000531*^9, {
3.691133424416461*^9, 3.6911334704928827`*^9}, 3.691133625128286*^9, {
3.6911336555669107`*^9, 3.691133685127342*^9}, {3.6911337267803173`*^9,
3.691133885233712*^9}, {3.691133956160441*^9, 3.691134000691243*^9}, {
3.6913185174671392`*^9, 3.691318583669483*^9}, {3.6913186153741198`*^9,
3.6913186812813663`*^9}, {3.691318715976606*^9, 3.6913187260212393`*^9},
3.691318766698841*^9, 3.6913188525969477`*^9, 3.6913219780614777`*^9, {
3.691322019567603*^9, 3.6913220415569973`*^9}, {3.691322086875514*^9,
3.69132211099693*^9}, {3.691322152144765*^9, 3.691322207791617*^9}, {
3.6913222381851187`*^9, 3.6913224458165293`*^9}, {3.691322607833271*^9,
3.6913226212577343`*^9}, 3.69363773272093*^9, 3.693637764765327*^9,
3.6936378703506203`*^9, 3.6936382659391317`*^9, 3.693638323614852*^9,
3.693638452554031*^9, 3.693638516113554*^9, 3.693639584448216*^9,
3.693639783240323*^9, 3.693639919775824*^9, {3.6936399602398243`*^9,
3.6936399770253763`*^9}, 3.693655705227008*^9, {3.693656063127898*^9,
3.69365610875527*^9}, {3.693656157101256*^9, 3.693656166362713*^9}, {
3.693656203138733*^9, 3.6936562309893713`*^9}, 3.6936563020406313`*^9,
3.6936599200290413`*^9, 3.693660057544281*^9, 3.6936601185836782`*^9,
3.699291271237254*^9, 3.69929130520506*^9, {3.699291474459896*^9,
3.699291613842441*^9}, 3.6992937576773987`*^9, 3.709997143675796*^9,
3.710821674044623*^9}],
Cell[CellGroupData[{
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"detJ=\"\>", "\[InvisibleSpace]",
RowBox[{"-", "1.`"}]}],
SequenceForm["detJ=", -1.],
Editable->False]], "Print",
CellChangeTimes->{
3.6936377326316032`*^9, 3.69363776468465*^9, 3.693637870276416*^9,
3.693638265862575*^9, 3.693638323543659*^9, 3.693638452476462*^9,
3.693638516035411*^9, 3.693639584372096*^9, 3.693639783167124*^9,
3.693639919699872*^9, {3.6936399601651697`*^9, 3.693639976948839*^9},
3.6936557051538982`*^9, {3.6936560630382977`*^9, 3.693656108682744*^9}, {
3.69365615702454*^9, 3.693656166280839*^9}, {3.693656203062585*^9,
3.693656230917675*^9}, 3.6936563019593763`*^9, 3.6936599199355907`*^9,
3.693660057456155*^9, 3.693660118510831*^9, 3.699291271142812*^9,
3.6992913051174173`*^9, {3.699291474379764*^9, 3.699291613762444*^9},
3.699293757592042*^9, 3.7099971436970243`*^9, 3.7108216740627823`*^9}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"The zero crossing of P is z0=\"\>", "\[InvisibleSpace]",
"0.06647087110104707`"}],
SequenceForm["The zero crossing of P is z0=", 0.06647087110104707],
Editable->False]], "Print",
CellChangeTimes->{
3.6936377326316032`*^9, 3.69363776468465*^9, 3.693637870276416*^9,
3.693638265862575*^9, 3.693638323543659*^9, 3.693638452476462*^9,
3.693638516035411*^9, 3.693639584372096*^9, 3.693639783167124*^9,
3.693639919699872*^9, {3.6936399601651697`*^9, 3.693639976948839*^9},
3.6936557051538982`*^9, {3.6936560630382977`*^9, 3.693656108682744*^9}, {
3.69365615702454*^9, 3.693656166280839*^9}, {3.693656203062585*^9,
3.693656230917675*^9}, 3.6936563019593763`*^9, 3.6936599199355907`*^9,
3.693660057456155*^9, 3.693660118510831*^9, 3.699291271142812*^9,
3.6992913051174173`*^9, {3.699291474379764*^9, 3.699291613762444*^9},
3.699293757592042*^9, 3.7099971436970243`*^9, 3.710821674065319*^9}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"Two zero crossings of F are z1=\"\>", "\[InvisibleSpace]",
"0.09952238321285`", "\[InvisibleSpace]", "\<\", z2=\"\>",
"\[InvisibleSpace]", "0.3068413659813639`"}],
SequenceForm[
"Two zero crossings of F are z1=", 0.09952238321285, ", z2=",
0.3068413659813639],
Editable->False]], "Print",
CellChangeTimes->{
3.6936377326316032`*^9, 3.69363776468465*^9, 3.693637870276416*^9,
3.693638265862575*^9, 3.693638323543659*^9, 3.693638452476462*^9,
3.693638516035411*^9, 3.693639584372096*^9, 3.693639783167124*^9,
3.693639919699872*^9, {3.6936399601651697`*^9, 3.693639976948839*^9},
3.6936557051538982`*^9, {3.6936560630382977`*^9, 3.693656108682744*^9}, {
3.69365615702454*^9, 3.693656166280839*^9}, {3.693656203062585*^9,
3.693656230917675*^9}, 3.6936563019593763`*^9, 3.6936599199355907`*^9,
3.693660057456155*^9, 3.693660118510831*^9, 3.699291271142812*^9,
3.6992913051174173`*^9, {3.699291474379764*^9, 3.699291613762444*^9},
3.699293757592042*^9, 3.7099971436970243`*^9, 3.7108216740684967`*^9}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"Two steady states of the SSN are re1=\"\>",
"\[InvisibleSpace]", "0.001016246071242415`",
"\[InvisibleSpace]", "\<\", ri1=\"\>", "\[InvisibleSpace]",
"0.0009857398227712216`", "\[InvisibleSpace]", "\<\" and re2=\"\>",
"\[InvisibleSpace]", "0.4714619577224822`",
"\[InvisibleSpace]", "\<\", ri2=\"\>", "\[InvisibleSpace]",
"0.028889612879877187`"}],
SequenceForm[
"Two steady states of the SSN are re1=", 0.001016246071242415, ", ri1=",
0.0009857398227712216, " and re2=", 0.4714619577224822, ", ri2=",
0.028889612879877187`],
Editable->False]], "Print",
CellChangeTimes->{
3.6936377326316032`*^9, 3.69363776468465*^9, 3.693637870276416*^9,
3.693638265862575*^9, 3.693638323543659*^9, 3.693638452476462*^9,
3.693638516035411*^9, 3.693639584372096*^9, 3.693639783167124*^9,
3.693639919699872*^9, {3.6936399601651697`*^9, 3.693639976948839*^9},
3.6936557051538982`*^9, {3.6936560630382977`*^9, 3.693656108682744*^9}, {
3.69365615702454*^9, 3.693656166280839*^9}, {3.693656203062585*^9,
3.693656230917675*^9}, 3.6936563019593763`*^9, 3.6936599199355907`*^9,
3.693660057456155*^9, 3.693660118510831*^9, 3.699291271142812*^9,
3.6992913051174173`*^9, {3.699291474379764*^9, 3.699291613762444*^9},
3.699293757592042*^9, 3.7099971436970243`*^9, 3.710821674071515*^9}]
}, Open ]],
Cell[BoxData[
GraphicsBox[{{{}, {
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBoQFe/iFib1JlAgAAABkAAAACAAAA120TQrjj1D9OgEyh/1i5v98+9ghH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"]]},
{Arrowheads[{{0.048787133701693464`, 1.}}], ArrowBox[CompressedData["
1:eJwBUQGu/iFib1JlAgAAABQAAAACAAAAQlRrs0FPxD9cDXcG31p1v/ez2eer
QcM/IuSIQicfcr8SyyaFGtHBPzRXbOyaaGy/z04Z0elzwD8OLS67bsdlv/Qd
hLokVb4/C1/POlYwYL/EtmN2Geu7P9IEkGm78Va/AMRq0jXTuD+9O1gQhj1I
v/1NMjsFA7Y/mFmsq/jXKr+5VLqwh3qzP4KZnXSDzCo/NtgCM705sT8wdb4P
rvs/P0BS1op2bq4/Lih0lMiERj9KMKXWLtOqPxTxHcKZoks/ikpySaOhpz9H
ldyQSldPP/+gPePT2aQ/ZQpYgG3RUD/YTs9vPjmgP9wGXQ0xGVI/RQy1wIZG
mT/qIbAze8JSP8qmWn6PVI0/pfWGvVP6Uj/sF+2MmZCBP2ZdoteYd1I/cjFu
2MXKdT/36uUU3dRRP79iu3b1l2w/hN8oQxBTUT+BEpqf
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.03796221951574091, 1.}}],
ArrowBox[{{0.10547106057913577`, -0.09901426017722878}, {
0.10368204493902007`, -0.09546979172031379}, {
0.10012322585537885`, -0.08923763437073091}, {
0.09659651737443999, -0.08335121645364696}, {
0.08963943222066928, -0.07261559891697572}, {
0.08281078947770797, -0.0632629391103001}, {
0.07611058914555602, -0.05529323703362007}, {
0.06967075109305376, -0.0483943603803976}, {
0.06362319518904147, -0.04225417684409465}, {
0.05796792143351917, -0.03687268642471124}, {
0.052704929826486835`, -0.03224988912224734}, {
0.05133752150609555, -0.031104694525135406`}, {0.05, -0.03}, {
0.04219472598693064, -0.023997711014995565`}, {
0.035526046080873605`, -0.019169759603389864`}, {
0.02937824788280505, -0.014827761140325791`}, {
0.02427221310071347, -0.011457668574344985`}}]}},
{GrayLevel[0],
{Arrowheads[{{0.05220759869924316, 1.}}], ArrowBox[CompressedData["
1:eJwBgQF+/iFib1JlAgAAABcAAAACAAAAkjFhT+YRw7/6SXc0PDKzvwGYjmcc
N8K/hl2sjARTsr8Y5qDFDVzBvzIo+hmIc7G/jV26jKiKwL8NzbZ06J2wv7r8
tXnZhb+/MZjEOUukr78TkQWstAm+v6dK+SR/IK6/67HPhmNLu7+vzPvLE1Sr
vwXNSPUEb7q/rLQnu0pzqr+amZmZmZm5v5qZmZmZmam/dkshVHUXt7+dTcgp
qAqnv2hZAQMx1LS/wvB2z+i7pL98aSk3b62yv0qJa89OiqK/2X3hdbK/sL+X
DOyD/5Kgv1xMyG9UCq6/Jlj6fCmgnb9f5NfrC/Cqv1QyR6FQd5q/QyIfBqOn
pb/0cCtkwReVv4DvMFReTqC/ZtgY3hVVj7/H47STzZKYv3TRfEBXNoe/Jq1j
QLkWjL/QMRHxo1R5vwQY2qafxn+/bInb2R+Gar/lx0iC7Zxwv0El7goWX1e/
gCUqWW1lX7+uB25fe6c5v2ANNDBzWka/MV3MNvf0KT/pM8Mz
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.04739410664348743, 1.}}], ArrowBox[CompressedData["
1:eJxTTMoPSmViYGAQBmIQPckw0f+Z4OH9EHqzvcyxBH47y0P7IfQm+9C7pXP3
xx7cD6E32gdd8mL53H1gP4TeYK/ltb99Q/v+/RB6vb3t6owd97j27YfQ6+yZ
FljppXnv3g+hV9vvbXK3Y8vftR9Cr7KfNRMEdu6H0Cvtu9/JLfggsn3/lKzA
ks8iy+0N66s3rTu/ZX/Dsj07j55fYs/K9my18fJN+2+xOghVL19kb16ZU+y2
Y8N+gTWfJ3zbscC+d9eqlbK/1u7vlJQ0fP5nrn1u7jnzzPur9puZ14tHP5ll
v1rmxuoNM5bun/zqyISyJVPtk8x3WvxzXbDfu+lKYGfCBPsDU/2PPZw4Yz93
/vcfpz532B8sN2Bu8OjZXzf3Vbckc509AB93nIU=
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJxTTMoPSmViYGCQBGIQDQMOnrdtHH3O2sP4UbUHZh6bewbOPxvzYZruytNw
vtQiwUuz9p6C8xedn6/49+ZJOP9wuliM898TcP6F63smVkcch/NdP7EUO58/
CufLb3/3f1biETjfqHTiXqbUw3B+hPjk3azFh+D8yXM//1zcfRDOf8S+ueLu
ugNwfrXg3DwXrX1w/hXj0++We+9G2K/AI6qWvwvOnzUTBHbae3c8Tj/yvsGO
7+4Chr5T2+z7Dk/w0jDZaGcl7x+b57XF3uDYRZFbDafsFp9YfOzc2432Vhll
nPvdH9jxNnZNituw3v6VjgrLl6APdldOPwiXZF5jfy3wbeXehX/slusfyTp+
eIX9jyTGtnOdAvbNT82Wxscttv/o4J4VJC9nP5n5wYqTvfPsAUwlhgM=
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBUQGu/iFib1JlAgAAABQAAAACAAAAC9X33wsU2T9ASds8QUzNP13jjUjo
ctg/cacLastSzD+a05Jwcc/XPzMrjClFWss/C0moZi8v1z/0SSKwPmvKP+Rh
IaUOktY/8sMrZpCEyT9UPFGm+/fVP2lZBrQSpcg/X9g3avZg1T9aCrKZxczH
PwE21fD+zNQ/xNYuF6n7xj8+VSk6FTzUP6i+fCy9McY/FDY0Rjmu0z8GwpvZ
AW/FP4PY9RRrI9M/3eCLHnezxD+LPG6mqpvSPy0bTfsc/8M/s91eKVBA0j/E
PVCEJofDP9M1y1BJ5tE/RDs0hJwRwz/4CheNNjbRP/bGnujNLcI/+7tRW3KL
0D9EvowosVPBP7iR9nb5y88/LiH+Q0aDwD83Yydbq4vOP2jf5XUaeb8/cOw1
Y/pVzT+sU9YaDP+9PwrUtpC/KM0/PiJQSM7IvT8UO52r
"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBgQF+/iFib1JlAgAAABcAAAACAAAAMo79Tzazyz/CfOXgmwu8Pxgm7N5v
Css/2cHLiRpFuz+wM3F82k/KP8DGkKzta7o/mpmZmZmZyT+amZmZmZm5PxHM
JzXeRMg/YvUBEjcbuD8CxZrYOQDHP9nEanVNtLY/BxbNYIPKxT/IsC5gfGG1
P/DjddkdpMQ/RNaE8+MjtD9ve1EVWH3DP057yEAr5bI/ASMJyCJlwj8EWXmq
armxP6banPF9W8E/Z2+XMKKgsD9cogySaWDAP+d8RaajNa8/IgYwpWPlvj+O
lPtrakutP2AL/bhFIr0/9C0W+g9+qz92VIBfeXe7Px1JlVCUzak/X+G5mP7k
uT8G5nhv9zmoP0awxKtRALc/jPsqZeRbpT+nYZLakmu0P/DE6Tlh1qI/vWBU
OrUHsj80BUQo04ugPwI3zc8I3a8/FjJ3unsknT9HSBdQXymsP5z12D0Is5k/
phkMf8zdqD+jSeVmEaOWPxVq3e4DWaQ/Rp64mBVzkj90TLMC
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.04980758923431585, 1.}}],
ArrowBox[{{0.6143237493504701, 0.2288896128798772}, {
0.6103941293128664, 0.2212560585374692}, {0.6061296548980218,
0.21270365983713707`}, {0.602963825494553, 0.20624184358016046`}, {
0.6, 0.2}, {0.5950690216482007, 0.18816720117156993`}, {
0.5910471041641356, 0.17714468302569988`}, {0.5875001069396509,
0.16650680400874934`}, {0.5849029502343271, 0.15663820324963784`}, {
0.58330415415719, 0.14749411008091917`}, {0.5827522388172657,
0.13902975383514732`}, {0.5833424570349939, 0.13120826423825288`}, {
0.5851700616308145, 0.12399277101616661`}, {0.5907926374444974,
0.11419732800396853`}, {0.6002951145025434, 0.10562296103374656`}, {
0.606873186625822, 0.10178279624476518`}, {0.6151649753154309,
0.09822613082705497}, {0.6214619577224821, 0.09616615799384397}}]}},
{GrayLevel[0],
{Arrowheads[{{0.06249999999999999, 1.}}], ArrowBox[CompressedData["
1:eJwBoQFe/iFib1JlAgAAABkAAAACAAAAnVHVzIte4j9ASds8QUzNP8aSoXtm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"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBcQGO/iFib1JlAgAAABYAAAACAAAAPYtbeC6I2j/eNjGlU1+3PykuWsoR
K9o/psWNCdSmtj9qeVRKporZP82fxiyff7U/Ku9v1rLy2D9Ug569Znm0P3Nl
BMK8Wdg/KfaWeBV/sz9G3BENxL/XP0/4r12rkLI/oFOYt8gk1z/EielsKK6x
P4bLl8HKiNY/iqpDpozXsD/zQxAryuvVP55avgnYDLA/6rwB9MZN1T8JNLMu
FZyuP2o2bBzBrtQ/ctEqnkg2rT+D7tfjwA/UP1HtczVj46s/RyPNic5x0z9+
5x7IfZ6qP7XUSw7q1NI/9r8rVphnqT/MAlRxEznSP7p2mt+yPqg/ja3lskqe
0T/KC2tkzSOnP/jUANOPBNE/J3+d5OcWpj8NeaXR4mvQP9DQMWACGKU/mDOn
XYeozz/GACjXHCekP5tEA9Bkfc4/2gmHTqNBoz9X+0v1XVjNP+PmVcsBZaI/
RmjOT7G2zD9hP+8Iq+2hP8uDsnk=
"]]},
{Arrowheads[{{0.042463331573387546`, 1.}}],
ArrowBox[{{0.2112687722550353, 0.032645303902924354`}, {
0.20355028970881386`, 0.03128187013565347}, {0.19535345196583928`,
0.02986848225538536}, {0.18734302166060068`, 0.02852256746593304}, {
0.17951899879309802`, 0.027244125767296522`}, {0.17196553741307236`,
0.02603285396023993}, {0.16464182570906716`, 0.024868328642426062`}, {
0.15754786368108253`, 0.023750549813854938`}, {0.15068365132911835`,
0.02267951747452653}, {0.1440491886531747, 0.02165523162444086}, {
0.13764447565325155`, 0.020677692263597922`}, {0.13146951232934892`,
0.019746899391997714`}, {0.12552429868146672`, 0.01886285300964023}, {
0.11428390584867232`, 0.01720893913427954}, {0.10388408258977677`,
0.015689890059141943`}, {0.09432482890478003,
0.014305705784227428`}, {0.08560614479368203,
0.013056386309535989`}, {0.07763404975940438,
0.011922006352514558`}}]}},
{GrayLevel[0],
{Arrowheads[{{0.06249999999999998, 1.}}], ArrowBox[CompressedData["
1:eJwBkQFu/iFib1JlAgAAABgAAAACAAAAMAKsLzqU2j9OgEyh/1i5v0aJcVvR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"]]},
{Arrowheads[{{0.007299639146413189, 1.}}],
ArrowBox[{{0.5984833738636893, -0.003661046977096194}, {
0.6018040217686544, -0.0031065145693504425`}, {
0.6103220930095248, -0.001769267139233463}, {
0.6193682875981826, -0.0004290555784392143}, {
0.6214619577224821, -0.00013533577139013454`}}]}}}},
GraphicsComplexBox[CompressedData["
1:eJxF2Hk0lH3YB/AhFEmiQtlCRPbtQcwV2VIPomxPhYip7DvZspU1ZUv2JbtC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"], {{}, {},
TagBox[
TooltipBox[
{RGBColor[1, 0, 0], Thickness[0.01],
LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51,
52, 53}],
LineBox[{54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68,
69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85,
86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101,
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115,
116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128,
129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142,
143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155,
156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169,
170, 171, 172, 173}],
LineBox[{174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185,
186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199,
200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212}]},
RowBox[{
RowBox[{
RowBox[{"-", "x"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"0.1`", "\[VeryThinSpace]"}], "+",
RowBox[{"1.5`", " ", "x"}], "-", "y"}], ")"}], "3"], " ",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"0.1`", "\[VeryThinSpace]"}], "+",
RowBox[{"1.5`", " ", "x"}], "-", "y"}], "]"}]}]}],
"\[Equal]", "0"}]],
Annotation[#, -$CellContext`x + (0.1 +
1.5 $CellContext`x - $CellContext`y)^3
HeavisideTheta[0.1 + 1.5 $CellContext`x - $CellContext`y] == 0,
"Tooltip"]& ],
TagBox[
TooltipBox[
{RGBColor[0, 0, 1], Thickness[0.01], LineBox[CompressedData["
1:eJwNztciQgEAANAbERlFZIZKyf4Xr976gHytEYqUEdkjqzgP5/2ki3s7pVAQ
BLvsc8AhR5Q55oRTKlQ545waF9RpcMkV19zQ5JY7WtzzwCNPPPPCK2+880Gb
T7745odfOnT5I5AO0UMvYfroJ8IAg0QZYpgRRokRZ4xxEkwwSZIppplhljnm
SbHAIkukyZBlmRx5ViiwyhrrbLDJFtv8A8uLLfU=
"]],
LineBox[{304, 305, 306, 307, 308}]},
RowBox[{
RowBox[{
RowBox[{"-", "y"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"0.1`", "\[VeryThinSpace]"}], "+",
RowBox[{"0.5`", " ", "x"}], "-", "y"}], ")"}], "3"], " ",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"0.1`", "\[VeryThinSpace]"}], "+",
RowBox[{"0.5`", " ", "x"}], "-", "y"}], "]"}]}]}],
"\[Equal]", "0"}]],
Annotation[#, -$CellContext`y + (0.1 +
0.5 $CellContext`x - $CellContext`y)^3
HeavisideTheta[0.1 + 0.5 $CellContext`x - $CellContext`y] == 0,
"Tooltip"]& ]}]},
AspectRatio->1,
DisplayFunction->Identity,
Epilog->{
PointSize[0.05],
PointBox[{{0.001016246071242415, 0.0009857398227712216}, {
0.4714619577224822, 0.028889612879877187`}}, VertexColors -> {
GrayLevel[0],
RGBColor[0, 0, 1]}]},
Frame->True,
FrameTicks->{{None, None}, {None, None}},
GridLines->{{{0.001016246071242415,
GrayLevel[0]}, {0.4714619577224822,
RGBColor[0, 0, 1]}}, {{0.0009857398227712216,
GrayLevel[0]}, {0.028889612879877187`,
RGBColor[0, 0, 1]}}},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
Method->{
"DefaultBoundaryStyle" -> Automatic, "TransparentPolygonMesh" -> True},
PlotRange->{{-0.161865110183253,
0.6343433139769776}, {-0.11189561643172423`, 0.24177096913437263`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.05],
Scaled[0.05]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.6699768032594643`*^9, 3.669976811777919*^9}, {
3.6699768718509502`*^9, 3.6699768979311953`*^9}, {3.671093452586643*^9,
3.6710935102663813`*^9}, {3.6711927175580587`*^9, 3.671192727770483*^9}, {
3.671192822041162*^9, 3.6711928386814823`*^9}, {3.673068247131949*^9,
3.673068356813676*^9}, 3.673068597293851*^9, 3.67306863268204*^9, {
3.673068673506373*^9, 3.6730687676141567`*^9}, 3.673068804911664*^9, {
3.673069006639491*^9, 3.673069116608088*^9}, 3.673069149271153*^9,
3.673091493191065*^9, 3.6730917428665037`*^9, 3.673091777141881*^9,
3.673091827941276*^9, 3.6730918727287903`*^9, 3.673092416709937*^9,
3.6730924734290743`*^9, {3.682230352723344*^9, 3.682230364360816*^9},
3.6822304016284237`*^9, 3.682230452079362*^9, 3.68223067486692*^9,
3.682230741442252*^9, 3.68223078479597*^9, 3.682230913608121*^9, {
3.682230949853684*^9, 3.6822309720720263`*^9}, {3.682231015561976*^9,
3.682231226074185*^9}, {3.682231265091152*^9, 3.682231336632937*^9}, {
3.682231393766885*^9, 3.68223140917111*^9}, {3.682231562412106*^9,
3.682231590222247*^9}, 3.6911316002285423`*^9, 3.6911316518605947`*^9,
3.691131837898481*^9, 3.69113197292867*^9, 3.691132192737213*^9, {
3.69113233006488*^9, 3.6911323414242353`*^9}, 3.691132400528872*^9,
3.6911324624080343`*^9, {3.6911325007837067`*^9, 3.691132528614489*^9},
3.691132565100687*^9, 3.691132595515601*^9, 3.69113271312779*^9,
3.691132791145338*^9, {3.691132930436285*^9, 3.691132940427868*^9}, {
3.6911329992188873`*^9, 3.691133022414216*^9}, 3.691133059462538*^9,
3.691133096502254*^9, 3.691133128741259*^9, 3.691133366000531*^9, {
3.691133424416461*^9, 3.6911334704928827`*^9}, 3.691133625128286*^9, {
3.6911336555669107`*^9, 3.691133685127342*^9}, {3.6911337267803173`*^9,
3.691133885233712*^9}, {3.691133956160441*^9, 3.691134000691243*^9}, {
3.6913185174671392`*^9, 3.691318583669483*^9}, {3.6913186153741198`*^9,
3.6913186812813663`*^9}, {3.691318715976606*^9, 3.6913187260212393`*^9},
3.691318766698841*^9, 3.6913188525969477`*^9, 3.6913219780614777`*^9, {
3.691322019567603*^9, 3.6913220415569973`*^9}, {3.691322086875514*^9,
3.69132211099693*^9}, {3.691322152144765*^9, 3.691322207791617*^9}, {
3.6913222381851187`*^9, 3.6913224458165293`*^9}, {3.691322607833271*^9,
3.6913226212577343`*^9}, 3.69363773272093*^9, 3.693637764765327*^9,
3.6936378703506203`*^9, 3.6936382659391317`*^9, 3.693638323614852*^9,
3.693638452554031*^9, 3.693638516113554*^9, 3.693639584448216*^9,
3.693639783240323*^9, 3.693639919775824*^9, {3.6936399602398243`*^9,
3.6936399770253763`*^9}, 3.693655705227008*^9, {3.693656063127898*^9,
3.69365610875527*^9}, {3.693656157101256*^9, 3.693656166362713*^9}, {
3.693656203138733*^9, 3.6936562309893713`*^9}, 3.6936563020406313`*^9,
3.6936599200290413`*^9, 3.693660057544281*^9, 3.6936601185836782`*^9,
3.699291271237254*^9, 3.69929130520506*^9, {3.699291474459896*^9,
3.699291613842441*^9}, 3.6992937576773987`*^9, 3.709997143675796*^9,
3.7108216743525457`*^9}]
}, Open ]],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.691322590134802*^9, 3.691322590175091*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{"Figure", " ", "2",
RowBox[{"(", "C", ")"}]}], ",", " ",
RowBox[{"three", " ", "steady", " ", "states"}]}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Clear", "[",
RowBox[{
"Jee", ",", "Jei", ",", "Jie", ",", "Jii", ",", "ge", ",", "gi", ",", "n",
",", "te", ",", "ti", ",", "cplus", ",", "F", ",", "P", ",", "Z", ",",
"z0", ",", "Z", ",", "re1", ",", "ri1", ",", "re2", ",", "ri2", ",",
"re3", ",", "ri3", ",", "plot1", ",", "plot2", ",", "plot3", ",",
"plot4", ",", "Ge", ",", "Gi"}], "]"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{"**", "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "********)"}],
"\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{"SSN", " ", "parameters"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**"}], "********)"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Jee", "=", "1.1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jei", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jie", "=", "0.5"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jii", "=", "0.1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"n", "=", "3"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"ge", "=", "0.2"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"gi", "=", "0.01"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"te", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ti", "=", "1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"detJ", "=",
RowBox[{
RowBox[{
RowBox[{"-", "Jee"}], "*", "Jii"}], "+",
RowBox[{"Jei", "*", "Jie"}]}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"cplus", "=", " ",
RowBox[{
RowBox[{
RowBox[{"-",
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}], "*", "Jii", "*", "ge"}], "+",
"gi"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
RowBox[{"Characteristic", " ", "function", " ", "for", " ", "detJ"}],
">", "0"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"P", "[", "z_", "]"}], "=",
RowBox[{
RowBox[{"detJ", "*",
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"z", "^", "n"}], ",",
RowBox[{"z", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"z", "\[LessEqual]", "0"}]}], "}"}]}], "}"}], "]"}]}],
"+",
RowBox[{
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jii", "*", "z"}], "+",
"cplus"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"F", "[", "z_", "]"}], "=",
RowBox[{
RowBox[{"Jee", "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"z", "^", "n"}], ",",
RowBox[{"z", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"z", "\[LessEqual]", "0"}]}], "}"}]}], "}"}], "]"}]}],
"-",
RowBox[{"Jei", "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"P", "[", "z", "]"}], ")"}], "^", "n"}], ",",
RowBox[{
RowBox[{"P", "[", "z", "]"}], ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{
RowBox[{"P", "[", "z", "]"}], "\[LessEqual]", "0"}]}], "}"}]}],
"}"}], "]"}]}], "-", "z", "+", "ge"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"plot1", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"P", "[", "z", "]"}], ",",
RowBox[{"{",
RowBox[{"z", ",",
RowBox[{"-", "0.01"}], ",", ".2"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<z\>\"", ",", "\"\<P(z)\>\""}], "}"}]}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"Directive", "[",
RowBox[{"Blue", ",", "Bold", ",",
RowBox[{"FontFamily", "\[Rule]", "\"\<Helvetica\>\""}]}], "]"}]}]}],
RowBox[{"(*",
RowBox[{",",
RowBox[{"Ticks", "\[Rule]", "None"}]}], "*)"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot2", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"F", "[", "z", "]"}], ",",
RowBox[{"{",
RowBox[{"z", ",",
RowBox[{"-", "0.01"}], ",", "1.45"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<z\>\"", ",", "\"\<F(z)\>\""}], "}"}]}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"Directive", "[",
RowBox[{"Blue", ",", "Bold", ",",
RowBox[{"FontFamily", "\[Rule]", "\"\<Helvetica\>\""}]}], "]"}]}]}],
RowBox[{"(*",
RowBox[{",",
RowBox[{"Ticks", "\[Rule]", "None"}]}], "*)"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{"GraphicsRow", "[",
RowBox[{"{",
RowBox[{"plot1", ",", "plot2"}], "}"}], "]"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<detJ=\>\"", ",", "detJ"}], "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"z0", "=",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{"P", "[", "z", "]"}], "\[Equal]", "0"}], ",", "z"}], "]"}]}],
";"}], " ",
RowBox[{"(*",
RowBox[{"Zero", " ", "crossing", " ", "of", " ", "P"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<The zero crossing of P is z0=\>\"", ",", " ",
RowBox[{"z", "/.",
RowBox[{"z0", "[",
RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], " ", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Z", "=",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{"F", "[", "z", "]"}], "\[Equal]", "0"}], ",", "z"}], "]"}]}],
";"}], " ",
RowBox[{"(*",
RowBox[{"Zero", " ", "crossings", " ", "of", " ", "F"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<Three zero crossings of F are z1=\>\"", ",", " ",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ",", "\"\<, z2=\>\"", ",",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ",", "\"\<, z3=\>\"", ",",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "3", "]"}], "]"}]}]}], "]"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"Steady", " ", "states", " ", "in", " ", "the", " ", "phase", " ",
"plane"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re1", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}], " ",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"ri1", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"detJ", "*",
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jii", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}]}], "+", "cplus"}], ")"}],
"^", "n"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re2", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}], " ",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"ri2", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"detJ", "*",
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jii", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}]}], "+", "cplus"}], ")"}],
"^", "n"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re3", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "3", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}], " ",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"ri3", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"detJ", "*",
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "3", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jei", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jii", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "3", "]"}], "]"}]}], ")"}]}], "+", "cplus"}], ")"}],
"^", "n"}]}], ";"}],
RowBox[{"(*",
RowBox[{"steady", " ", "states"}], "*)"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{
"\"\<Three steady states of the SSN are re1=\>\"", ",", " ", "re1",
",", " ", "\"\<, ri1=\>\"", ",", " ", "ri1", ",", " ", "\"\<; re2=\>\"",
",", " ", "re2", ",", " ", "\"\<, ri2=\>\"", ",", " ", "ri2", ",",
" ", "\"\<; re3=\>\"", ",", " ", "re3", ",", " ", "\"\<, ri3=\>\"",
",", " ", "ri3"}], "]"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"Right", " ", "hand", " ", "side", " ", "of", " ", "the", " ", "SSN", " ",
"equations"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "x"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Jee", "*", "x"}], "-",
RowBox[{"Jei", "*", "y"}], "+", "ge"}], ")"}], "^", "n"}], "*",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"Jee", "*", "x"}], "-",
RowBox[{"Jei", "*", "y"}], "+", "ge"}], "]"}]}]}], ")"}], "*",
RowBox[{"te", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Gi", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "y"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Jie", "*", "x"}], "-",
RowBox[{"Jii", "*", "y"}], "+", "gi"}], ")"}], "^", "n"}], "*",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"Jie", "*", "x"}], "-",
RowBox[{"Jii", "*", "y"}], "+", "gi"}], "]"}]}]}], ")"}], "*",
RowBox[{"ti", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Clear", "[",
RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}], ";"}],
RowBox[{"(*",
RowBox[{
"Define", " ", "the", " ", "plot", " ", "region", " ", "around", " ",
"the", " ", "steady", " ", "states"}], "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"a", "=",
RowBox[{"re1", "-", "1."}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"b", "=",
RowBox[{"re3", "+", ".5"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"c", "=",
RowBox[{"ri1", "-", ".3"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"d", "=",
RowBox[{"ri3", "+", "1."}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot3", "=",
RowBox[{"StreamPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x", ",", "y"}], "]"}], ",",
RowBox[{"Gi", "[",
RowBox[{"x", ",", "y"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "a", ",", "b"}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",", "c", ",", "d"}], "}"}], ",",
RowBox[{"StreamStyle", "\[Rule]", "Black"}], ",",
RowBox[{"StreamScale", "\[Rule]", "0.25"}], ",",
RowBox[{"StreamPoints", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "0.8"}], ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "0.4"}], ",",
RowBox[{"-", "0.25"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.3", ",",
RowBox[{"-", "0.25"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.6", ",",
RowBox[{"-", "0.25"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.6", ",", "2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"3", ",", "2.4"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1", ",", "0.5"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1.2", ",", "0.5"}], "}"}], ",",
RowBox[{"{",
RowBox[{"2.8", ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"3.2", ",", "1.7"}], "}"}]}], "}"}]}], ",",
RowBox[{"Epilog", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"PointSize", "[", "0.05", "]"}], ",",
RowBox[{"Point", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"re1", ",", "ri1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re2", ",", "ri2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re3", ",", "ri3"}], "}"}]}], "}"}], ",",
RowBox[{"VertexColors", "\[Rule]",
RowBox[{"{",
RowBox[{"Black", ",", "Blue", ",", "Red"}], "}"}]}]}], "]"}]}],
"}"}]}], ",",
RowBox[{"GridLines", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"re1", ",", "Black"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re2", ",", "Blue"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re3", ",", "Red"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"ri1", ",", "Black"}], "}"}], ",",
RowBox[{"{",
RowBox[{"ri2", ",", "Blue"}], "}"}], ",",
RowBox[{"{",
RowBox[{"ri3", ",", "Red"}], "}"}]}], "}"}]}], "}"}]}], ",",
RowBox[{"FrameTicks", "\[Rule]", "None"}]}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot4", "=",
RowBox[{"ContourPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "0"}], ",",
RowBox[{
RowBox[{"Gi", "[",
RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",",
RowBox[{"a", "-", ".1"}], ",",
RowBox[{"b", "+", ".05"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",",
RowBox[{"c", "-", ".03"}], ",",
RowBox[{"d", "+", ".025"}]}], "}"}], ",",
RowBox[{"ContourStyle", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"(*",
RowBox[{"Dashed", ","}], "*)"}],
RowBox[{"Red", ",",
RowBox[{"Thickness", "[", "0.01", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"Blue", ",",
RowBox[{"(*",
RowBox[{"Dashed", ","}], "*)"}],
RowBox[{"Thickness", "[", "0.01", "]"}]}], "}"}]}], "}"}]}]}],
"]"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"Show", "[",
RowBox[{"plot3", ",", "plot4"}], "]"}],
"\[IndentingNewLine]"}]}]], "Input",
CellChangeTimes->{{3.691134052939101*^9, 3.691134058397626*^9}, {
3.691134172906389*^9, 3.691134492805238*^9}, {3.691134536822394*^9,
3.691134536950247*^9}, {3.691134655850223*^9, 3.691134656192999*^9}, {
3.691134850477024*^9, 3.691134854957532*^9}, {3.691135032877783*^9,
3.6911350720922318`*^9}, {3.6911353047567053`*^9, 3.691135318856195*^9}, {
3.691135349392283*^9, 3.691135355897873*^9}, {3.691135391587961*^9,
3.691135397441846*^9}, {3.6911354717731533`*^9, 3.6911355432015038`*^9}, {
3.691135584039589*^9, 3.691135584616358*^9}, {3.6911356666101303`*^9,
3.6911358109630632`*^9}, {3.6912173644220877`*^9, 3.691217595518058*^9}, {
3.691420373197418*^9, 3.6914205607029676`*^9}, {3.691421841307733*^9,
3.691421892647883*^9}, {3.691422049939636*^9, 3.6914223577885847`*^9}, {
3.691422468057934*^9, 3.691422605512888*^9}, {3.691422636379649*^9,
3.691422639383772*^9}, {3.693639835595941*^9, 3.693639838141773*^9}, {
3.693639875476184*^9, 3.6936398815241833`*^9}, {3.693639992451497*^9,
3.6936400202991734`*^9}, {3.693655736279849*^9, 3.693655737201605*^9}, {
3.6936557898603363`*^9, 3.693655800924857*^9}, {3.693655861716138*^9,
3.693655883011608*^9}, {3.693655918581468*^9, 3.693655927109304*^9},
3.693655972610796*^9, {3.693656019860427*^9, 3.693656024755247*^9}, {
3.69365625427087*^9, 3.693656256632647*^9}, {3.6936564083263483`*^9,
3.693656628272683*^9}, {3.693656698021968*^9, 3.6936567475952682`*^9}, {
3.693656962494323*^9, 3.693656963443903*^9}, {3.693657344214891*^9,
3.693657350070036*^9}, {3.693657952525804*^9, 3.693657952597002*^9}, {
3.693659935213972*^9, 3.693659946749631*^9}, {3.693660029701886*^9,
3.693660030175029*^9}, {3.693660133982649*^9, 3.693660135267715*^9}, {
3.699293779037713*^9, 3.6992938132362022`*^9}, {3.709997187085375*^9,
3.7099972312268457`*^9}, {3.709997316899547*^9, 3.709997319983465*^9}}],
Cell[BoxData[
GraphicsBox[{{}, {InsetBox[
GraphicsBox[{{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.],
LineBox[{{-0.009999995714285715, -0.010999999571428574`}, \
{-0.009935589239311315, -0.010993558923931135`}, {-0.009871182764336916, \
-0.010987118276433696`}, {-0.009742369814388115, -0.010974236981438816`}, \
{-0.009484743914490515, -0.010948474391449055`}, {-0.008969492114695315, \
-0.010896949211469536`}, {-0.007938988515104913, -0.010793898851510495`}, \
{-0.00587798131592411, -0.010587798131592415`}, {-0.0014092453626965702`, \
-0.010140924536269661`}, {-0.00006696428571428572, -0.010006696428571433`}}],
LineBox[CompressedData["
1:eJwVynk41HkAx3FHpdiSdWw6FMqRo2glrfoUhVw51pLiQUaScc00jzGNazLN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"]]}, {}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox["\"z\"", TraditionalForm],
FormBox["\"P(z)\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
RGBColor[0, 0, 1], Bold, FontFamily -> "Helvetica"],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{-0.01, 0.2}, {-0.010999999571428574`,
0.013119999370857147`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}], {192., -116.80842387373012`},
ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}], InsetBox[
GraphicsBox[{{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.],
LineBox[{{-0.009999970204081632,
0.20999997020408165`}, {-0.009552191854259613,
0.20955219185425963`}, {-0.009104413504437593,
0.2091044135044376}, {-0.008208856804793553,
0.20820885680479356`}, {-0.006417743405505476,
0.20641774340550548`}, {-0.0028355166069293195`,
0.20283551660692933`}, {-0.0004655612244897959,
0.2004655612244898}}],
LineBox[{{0.004328936990222993, 0.19567115224503398`}, {
0.01865784418452762, 0.18134930040151415`}, {0.049726198906966695`,
0.15040905458099849`}, {0.07873570639055755,
0.12180121149314549`}, {0.0960302318288544, 0.10494389749528422`}}],
LineBox[CompressedData["
1:eJwVl3k81F8Xxw2RopItIlsI2UmFOoqksiX8JEmUJJKlKBKFJEq2pKzZkiyR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"]]}, {}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox["\"z\"", TraditionalForm],
FormBox["\"F(z)\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
RGBColor[0, 0, 1], Bold, FontFamily -> "Helvetica"],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{-0.01, 1.45}, {-0.21726186891061494`, 0.4269838452360828}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}], {576., -116.80842387373012`},
ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}]}, {}},
ContentSelectable->True,
PlotRangePadding->{6, 5}]], "Output",
CellChangeTimes->{
3.691134202135131*^9, {3.691134482072929*^9, 3.691134493232272*^9}, {
3.691135464444171*^9, 3.691135521071075*^9}, 3.69113555156861*^9,
3.69113558514855*^9, {3.691135669538349*^9, 3.691135811321965*^9}, {
3.691217397332892*^9, 3.6912175960938053`*^9}, {3.691420380059111*^9,
3.6914204165766563`*^9}, {3.6914204541994457`*^9, 3.691420561018105*^9}, {
3.691421852758523*^9, 3.691421893486292*^9}, {3.69142205105159*^9,
3.691422182787798*^9}, {3.691422217228775*^9, 3.69142235850133*^9},
3.6914224825225058`*^9, {3.691422513992503*^9, 3.691422606012048*^9},
3.691422640697515*^9, 3.6936400219527483`*^9, 3.693655825640711*^9, {
3.6936558663135967`*^9, 3.69365588348368*^9}, 3.6936563248986597`*^9,
3.6936565414858*^9, 3.6936565785533524`*^9, 3.693656612856802*^9, {
3.693656719623467*^9, 3.693656748824079*^9}, {3.693659939167927*^9,
3.693659947413575*^9}, 3.693660067741686*^9, 3.6936601360451717`*^9, {
3.699293797371296*^9, 3.699293815907547*^9}, 3.7099972335798903`*^9,
3.709997322525209*^9, 3.7108216867832747`*^9}],
Cell[CellGroupData[{
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"detJ=\"\>", "\[InvisibleSpace]", "0.39`"}],
SequenceForm["detJ=", 0.39],
Editable->False]], "Print",
CellChangeTimes->{
3.693640021907589*^9, 3.693655825566751*^9, {3.693655866233906*^9,
3.693655883402533*^9}, 3.69365632481562*^9, 3.693656541406289*^9,
3.6936565784681053`*^9, 3.693656612769046*^9, {3.693656719544258*^9,
3.693656748738892*^9}, {3.693659939086276*^9, 3.693659947332032*^9},
3.6936600676576223`*^9, 3.693660135962529*^9, {3.699293797285664*^9,
3.699293815817474*^9}, 3.7099972335988817`*^9, 3.70999732254827*^9,
3.710821686799358*^9}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"The zero crossing of P is z0=\"\>", "\[InvisibleSpace]",
"0.09649579305334417`"}],
SequenceForm["The zero crossing of P is z0=", 0.09649579305334417],
Editable->False]], "Print",
CellChangeTimes->{
3.693640021907589*^9, 3.693655825566751*^9, {3.693655866233906*^9,
3.693655883402533*^9}, 3.69365632481562*^9, 3.693656541406289*^9,
3.6936565784681053`*^9, 3.693656612769046*^9, {3.693656719544258*^9,
3.693656748738892*^9}, {3.693659939086276*^9, 3.693659947332032*^9},
3.6936600676576223`*^9, 3.693660135962529*^9, {3.699293797285664*^9,
3.699293815817474*^9}, 3.7099972335988817`*^9, 3.70999732254827*^9,
3.7108216868019657`*^9}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"Three zero crossings of F are z1=\"\>", "\[InvisibleSpace]",
"0.21021532821375397`", "\[InvisibleSpace]", "\<\", z2=\"\>",
"\[InvisibleSpace]", "0.855010954614683`",
"\[InvisibleSpace]", "\<\", z3=\"\>", "\[InvisibleSpace]",
"1.416996242803104`"}],
SequenceForm[
"Three zero crossings of F are z1=", 0.21021532821375397`, ", z2=",
0.855010954614683, ", z3=", 1.416996242803104],
Editable->False]], "Print",
CellChangeTimes->{
3.693640021907589*^9, 3.693655825566751*^9, {3.693655866233906*^9,
3.693655883402533*^9}, 3.69365632481562*^9, 3.693656541406289*^9,
3.6936565784681053`*^9, 3.693656612769046*^9, {3.693656719544258*^9,
3.693656748738892*^9}, {3.693659939086276*^9, 3.693659947332032*^9},
3.6936600676576223`*^9, 3.693660135962529*^9, {3.699293797285664*^9,
3.699293815817474*^9}, 3.7099972335988817`*^9, 3.70999732254827*^9,
3.710821686805283*^9}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"Three steady states of the SSN are re1=\"\>",
"\[InvisibleSpace]", "0.009289517143394582`",
"\[InvisibleSpace]", "\<\", ri1=\"\>", "\[InvisibleSpace]",
"3.140643980082845`*^-6", "\[InvisibleSpace]", "\<\"; re2=\"\>",
"\[InvisibleSpace]", "0.6250503995994064`",
"\[InvisibleSpace]", "\<\", ri2=\"\>", "\[InvisibleSpace]",
"0.032544484944664095`", "\[InvisibleSpace]", "\<\"; re3=\"\>",
"\[InvisibleSpace]", "2.845156080957054`",
"\[InvisibleSpace]", "\<\", ri3=\"\>", "\[InvisibleSpace]",
"1.912675446249655`"}],
SequenceForm[
"Three steady states of the SSN are re1=", 0.009289517143394582, ", ri1=",
3.140643980082845*^-6, "; re2=", 0.6250503995994064, ", ri2=",
0.032544484944664095`, "; re3=", 2.845156080957054, ", ri3=",
1.912675446249655],
Editable->False]], "Print",
CellChangeTimes->{
3.693640021907589*^9, 3.693655825566751*^9, {3.693655866233906*^9,
3.693655883402533*^9}, 3.69365632481562*^9, 3.693656541406289*^9,
3.6936565784681053`*^9, 3.693656612769046*^9, {3.693656719544258*^9,
3.693656748738892*^9}, {3.693659939086276*^9, 3.693659947332032*^9},
3.6936600676576223`*^9, 3.693660135962529*^9, {3.699293797285664*^9,
3.699293815817474*^9}, 3.7099972335988817`*^9, 3.70999732254827*^9,
3.7108216868085012`*^9}]
}, Open ]],
Cell[BoxData[
GraphicsBox[{{{}, {
{GrayLevel[0],
{Arrowheads[{{0.05501621018163476, 1.}}], ArrowBox[CompressedData["
1:eJwBoQFe/iFib1JlAgAAABkAAAACAAAAOY11eOaz77+BmnrJthINv7fMK2DV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"]]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBcQGO/iFib1JlAgAAABYAAAACAAAAOY11eOaz779EeEkLcNDzPyww31xf
qO+/HH4LmjvJ8z9DHleQlxHuv+pyNrr+yvI/4KrSCSCP7L/MqiMGdNnxP/7V
Ucn4IOu/vyXTfZv08D9OvdvQclrqv1FWicKHePA/mpmZmZmZ6b8AAAAAAADw
P+L2MtTR/ue/mrQ/SYb+7T9/0nhVyX3mvx4H16o7Hew/3modDbZE5b+VxWSQ
45XqP+LkpK7KG+S/Gh5OWr0i6T+MQA86BwPjv68QkwjJw+c/2H1cr2v64b9O
nTObBnnmP7Pjhb5VAOG/oFwnLmtA5T8DuYQXIxPgv0TnZd3rF+Q/lfuxdKdl
3r89Pe+oiP/iPw5kBU7Pvty/iV7DkEH34T/C0Kqo/rPZv3rCail/EOA/G7f3
K2D71r/ipPU2OLrcPyvZiCnWB9W/dg/rs8tJ2j+a6UgXXEHTvwEkGx2zEdg/
TdQrl41o0r9gyfb8sALXP1Gwv9E=
"]]},
{Arrowheads[{{0.013717455070407636`, 1.}}],
ArrowBox[{{-0.24075947613895926`,
0.3009493451736991}, {-0.21103286218628753`,
0.26379107773285937`}, {-0.17655092808087133`,
0.22068866010108917`}, {-0.14761397577015875`,
0.18451746971269845`}, {-0.12346253484283308`,
0.15432816855354137`}, {-0.08644818754411496, 0.1080602344301437}}]}},
{GrayLevel[0],
{Arrowheads[{{0.022258991582484795`, 1.}}],
ArrowBox[{{-0.47999497709975064`, -0.2999968593560199}, \
{-0.4257409489190487, -0.26608809175559767`}, {-0.41266982024881804`, \
-0.25791863637832485`}, {-0.4, -0.25}, {-0.37021990331225735`, \
-0.23138807341491202`}, {-0.34265400640424554`, -0.2141616945939112}, \
{-0.2916274790967962, -0.18228282920571837`}, {-0.2481755846097751, \
-0.15515967876952985`}, {-0.2111346538026976, -0.13207378424788488`}, \
{-0.17192790665556357`, -0.107700095831337}, {-0.13989613368785006`, \
-0.08786909282815744}}]}},
{GrayLevel[0],
{Arrowheads[{{0.033091445247477, 1.}}], ArrowBox[CompressedData["
1:eJwBYQGe/iFib1JlAgAAABUAAAACAAAAPfkhAajg0D9pjvUGJjPTv9F5wkyy
ctI/LOhqfiES0b+hchj4XNXSP/oT+bLzhtC/MzMzMzMz0z8AAAAAAADQv7xS
pXjGCdQ/aL+KkMZdzb/ZT3LXVr/UP84128iE8Mq/CG9uPp/r1T8ZX8YhNXjG
vy/Eep95oNY/n/8EzRq1wr9QioQQ3OnWPzd7rjsSF7+/Fxs+DWXi1T8IzxRM
dJ6yv3tgofXgB9M/LqJ751X8pb/b/YsAq7fOPxGiKJwmypm/q2WI5fBvxz+C
L0hC/6COv88z3xlVjcE/5HJhm2jggr9Z6M1TZNe5P/lfNs+KYXe/Ynd2RbTp
sj9/s+oZ/CBtvyvjx/E+yqs/4dTxlG87Yr9KHGj8ZpaiP4mt7VpJ+lK/T49+
IjcVmj9wKeOS6YxEvyl0BIh2eZM/h7Hrp8VdN79mkUayoD2OP5rJGvHipii/
/3CwZg==
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBkQFu/iFib1JlAgAAABgAAAACAAAAmuWrX1BA3z9pjvUGJjPTvxwecGT0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"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBUQGu/iFib1JlAgAAABQAAAACAAAADKtjbIed+j8aAtzpebi2vzA/5M9Q
B/s/mwkOMacgtr9khVBfe9L7P4z4rDL0/7S//E9y6kuu/D8XsAMcPsqzv/me
SXHCmv0/OjAS7YR/sr9t1Qq9emj+P1QU+bZ7YbG/btKfiEZI/z84xj7Ltyuw
vwBLBOoSHQBAzovGU3K8rb8OkKJPDJ8AQLwmzaX/8aq/ai7HkmIQAUA47x3A
OISov9K1hbiGiwFA7lbOsTLhpb9IJt7AeBACQPxd3nrtCKO/0H/QqzifAkBb
CJw20vafv0QBO6zvGwNAbYO/hFWgmr/K3zEsRqMDQP4P+6D80pS/Yxu1Kzw1
BECxW50Wjx2Nvxe0xKrR0QRAyHLpDtlOf79of1y11FoFQISP7oruxl6/gDQo
xlXvBUAumTvfivtxPy1UyXwvRwZA53to9WObgD8FDaGI
"]]},
{Arrowheads[{{0.027072825590305098`, 1.}}],
ArrowBox[{{2.859509365517104, 0.01459519242700926}, {
2.8611520154839267`, 0.01473785068129397}, {2.9037208136683264`,
0.018438887382579885`}, {2.9771913334375735`, 0.02484499418403508}, {
3.0567402744108474`, 0.03180993290141075}, {3.0987941528489937`,
0.03550196422856875}, {3.1423676365881468`, 0.039333703534706846`}, {
3.187460725628306, 0.04330515081982503}, {3.2340734199694716`,
0.04741630608392329}, {3.3147118788713836`, 0.05455210105608853}, {
3.345156080957054, 0.05725576397833474}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBUQGu/iFib1JlAgAAABQAAAACAAAAZtjKCdT46z8qCczIKE0HQA+jZx4q
Ues/jC8ZyqzBBkAL3UITb6bqP7R343mgMwZASJwl0vP/6T8wCLj5GakFQMTg
D1u4Xek//+CWSRkiBUB+qgGuvL/oPyACgGmengRA5ktKc58l6D++ArtGWR4E
QG0XOVP/juc/AXqPzvmgA0AQDc5N3PvmP+pn/QCAJgNA0SwJYzZs5j94zATe
664CQLB26pIN4OU/raelZT06AkCt6nHdYVflP4j535d0yAFAxoifQjPS5D8H
wrN0kVkBQP5Qc8KBUOQ/LAEh/JPtAEAHEV9g17/jP7YBUOoddQBAMzMzMzMz
4z8AAAAAAAAAQG6BvntgqeI/xVpEgG4a/z/uavg4gyPiP9nI3jtyO/4/wsRD
5Uyh4T/sbJg0iWL9Pyadru7inOE/mJuCzS5b/T9Uc5V+
"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBYQGe/iFib1JlAgAAABUAAAACAAAAr9KPoTDs4D8ozI5S0zT8P2RzM0FD
sOA/FRYTaP7Q+z+ItJQCdkDgP8+mLHK9Fvs/qxac4t+m3z+d7XrdG2H6P5Tv
vhpi0t4/fOr9qRmw+T/Q85GtcgPeP3Gdtde2A/k/XSMVmxE63T94BqJm81v4
Pzl+SOM+dtw/lCXDVs+49z9mBCyG+rfbP8L6GKhKGvc/SkqqjvlJ2j9+nnBI
Wen1P5ysNmfr7dg/0Mi2IVnH9D9eK9EP0KPXP7p56zNKtPM/j8Z5iKdr1j86
sQ5/LLDyP+sddXe2Q9U/VtaWlI+58T8q0QeDQSrUPxRQ+gUDz/A/T+Axq0gf
0z/nPHKmDeHvP1hL8+/LItI/6YKm+DU87j8DfBX+WqvQP+DYMyxmyus/zWeI
0gWozj9iXg4OD47pP9wqZVtnMcw/NJ2TAm+A5z9+8D5QlErKPwQrdO6o6uU/
oC6tig==
"]]},
{Arrowheads[{{0.030534288746036573`, 1.}}],
ArrowBox[{{0.18384511760979816`, 0.6130263596338863}, {
0.17097258258048928`, 0.5701076257988935}, {0.15710734659183642`,
0.5238783221072406}, {0.14433480290817466`, 0.48129185290739235`}, {
0.12179343333576129`, 0.4061326401990118}, {0.10279975562312227`,
0.3428004321055543}, {0.08678872869091594, 0.2894083501801976}, {
0.07328916975945166, 0.24437868254662123`}, {0.05662061742176015,
0.18865055871446784`}, {0.04385032422615069, 0.14559780099630046`}, {
0.026696183878988117`, 0.0861151647928122}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBoQFe/iFib1JlAgAAABkAAAACAAAAjs4tx63CBkDTwOBgyZP+PxLWXOFl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"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBsQFO/iFib1JlAgAAABoAAAACAAAAh9qo01s6BkCjI/1daaICQDDISmec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"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBcQGO/iFib1JlAgAAABYAAAACAAAA76K477QZ/D+GJNvxWVf7P1eQu+WT
7vs/tC1tpQc1+z/OnvduEGX7P1fXv2Inxvo/k3vLlN3d+j92laaLv1f6P9I9
DjH7WPo/muTWLurp+T+0/JYdadb5P1BBBlvBfPk/Ds3WTjXY+D+fFTiJ3aT4
P/WlQ/dA4/c/uvbni+TQ9z8wgJukT/f2P/jDXa0kAfc/NFSfCAMU9j/OWfHV
oTX2P9xaDCgnOfU/Sphm6Lxu9T8CzZ8HiGb0P3ZfgcfWrPQ/F/RydwvL8z8y
K5ulIBz0PyS/mPQRNPM/cO7IXDuO8z8/YW//f6HyP1S8+B45A/M/gg1VGDoT
8j8EqBgeLHvyPwD3p78kifE/oMQWjCb28T/SUMZ1JAPxP0ol4Zo6dPE/DE4O
ux2B8D8l3WV8evXwP8gh3g/1AvA/V/+SYvh58D9cHdjupiPuP4VZ8ys5GO8/
iNXeoA6K7T/mVnVoF3/uP+ibuU0=
"]]},
{Arrowheads[{{0.05934600718887245, 1.}}], ArrowBox[CompressedData["
1:eJwBYQGe/iFib1JlAgAAABUAAAACAAAANofWAVzX6z8R42ngh8zsP6zu5Q+7
suo/zZTWBTum6z8CkymdriDpP7o+nc1ND+o/IcMQ6VCm5z+EKVPXH47oP5oA
Z5R2QuY/FEwwxoch5z9iOaIbt/PkP+Fae4a9yOU/aVs4+6m44z9kCnsE+YLk
P1IHqDo7kOI/XEf1UV9P4z/8jOIwh3nhP2aMr7oKLeI/OuGJ0W1z4D/K4u8B
IxvhP7nxfyCe+d4/0FP86s8Y4D9Kd297sLbbP54b5C7Ew9w/LKtRW5HP2D8U
DDqOhbLZP/oCOASqONY/9rBCPBD01j9K9DO6Y+bTPy5CRoGQftQ/JviwIy/S
0T/eFsogMEvSP2ilCRq58M8/G+FRSc5U0D9s1EBmSaPMP4zCRsdOKM0/3knp
pYCtyT9/rwix7wPKP3qeAB7Nq8Q/qCh5CrGyxD8h0DS/cLHAP4ngFGxHd8A/
POWp6Q==
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBUQGu/iFib1JlAgAAABQAAAACAAAA54klFwuLBkANyhIRsZH+P/lwn2wG
MAZA/vJO9CQ6/j+xgSFoee0FQBYtWZZe8/0/wpMHXWCaBUDGCMhZ55X9P1U6
z9i4NQVAACB+g4Ef/T+iddDeRb4EQAC7M71hjPw/+wuSTUs0BEDUox4H+Nr7
P2hY3kup6ANAwCpdLJt2+z/WeK/TFJkDQG46Ch/HCvs/QAoK+/E1A0CmZeJ4
Y4H6P180myfdzgJAWURo2yzv+T8192JZ1mMCQIbWm0YjVPk/wVJhkN30AUAt
HH26RrD4PzFUq708gwFABVqTv2sF+D+yCFbSPRABQMHUZd5mVfc/RXBhzuCb
AEBjjPQWOKD2P+iKzbElJgBA64A/ad/l9T9VG8CQXmD/Pye3BXN4KPU/Nlu9
u0B2/j/kMwbSHmr0P3duu4MRVf4/Atn3SMtO9D9M4pQQ
"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBYQGe/iFib1JlAgAAABUAAAACAAAAJ+C4fwVo/T/E54FTMYvzPwWKQAty
p/w/6AC2j5Pq8j/Q1SixPP37PyQRkhMwW/I/Nt2kuFdV+z8bKdXztMzxPxTi
Ic/6r/o/HmeX4G8/8T/kJw2iXQ36P93q8Imus/A/GgqHTZ4w+T+nB8wDxOnv
P5LG3iD3Wfg/YREzbBp17j9MXRQcaIn3P+nyFk1gCe0/Rc4nP/G+9j88rHem
labrP9a9ihGv+vU/Km1jc/lN6j9S0K4avjz1P3xl6K7KAOk/uwWUWh6F9D8z
lQZZCb/nPw9eOtHP0/M/Ufy9cbWI5j/TfcX+WO/yP+X7WqUA++Q/tGsadsIU
8j/ax0ryZoLjP7MnOTcMRPE/MGCNWOge4j/QsSFCNn3wP+fEItiE0OA/wjd8
jyM+8D9zE0elLWfgPwAAAAAAAPA/AAAAAAAA4D+sAHEVRILvP6IYQYsXNd8/
Ynul0Q==
"]]},
{Arrowheads[{{0.04351210716419827, 1.}}],
ArrowBox[{{0.9259865303364014, 0.4408400084972125}, {
0.9083797830999565, 0.4269958259876611}, {0.8644407063686488,
0.3929349953957739}, {0.8223204493948774, 0.3612812191822749}, {
0.7818756995938148, 0.33190243870328673`}, {0.7429631443806346,
0.3046665953149324}, {0.70547758336605, 0.2794475786109175}, {
0.6693138161607749, 0.25611927818494784`}, {0.6234098966287911,
0.22801523710323063`}, {0.579704544227966, 0.2028370494694995}, {
0.5379926337623557, 0.18025616205804046`}, {0.4980690400360166,
0.1599440216431396}, {0.42376733585178605`, 0.12542018995799195`}, {
0.35716049777654446`, 0.09785397072401623}, {0.29826697968037147`,
0.07593261364930821}, {0.247263140119362,
0.058746412369017766`}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBsQFO/iFib1JlAgAAABoAAAACAAAAcQDBochA9T+btL0SuOLlPyz4NjAj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"]]},
{Arrowheads[{{0.06250000000000001, 1.}}], ArrowBox[CompressedData["
1:eJwBYQGe/iFib1JlAgAAABUAAAACAAAAfGcU+juTAEDP1u8wPz3ZP9UZRAiZ
ugBAkH6xn3dZ2T/kJgivOi0BQBsztjx2rdk/ieM9yheQAUC54P/4d/fZP6im
UhZ//AFA/tUWTUZK2j8/cEaTcHICQOkS+zjhpdo/UEAZQezxAkB9l6y8SArb
PxrNvwgwYANA96Mvb1hi2z94Kzlcw9gDQI4OqQLxw9s/bFuFO6ZbBEBI1xh3
Ei/cP/FcpKbY6ARAH/5+zLyj3D8MbZxhTWMFQEKFCC3kCd0/UONTbenoBUCS
nWeQZXrdP7y/ysmseQZADUec9kD13T9OAgF3lxUHQLSBpl92et4/HG8Fdyad
B0AhmuxfE+/eP84gKCLIMAhAtHyIf/Bu3z9gF2l4fNAIQGkper4N+t8/fuy0
o90kCUDIldk06iHgP8tSyHlDfAlAHdBgjjVI4D8J/6BvF4gJQF0zMpZpTeA/
OSSYdw==
"]]},
{Arrowheads[{{0.004420673066639869, 1.}}],
ArrowBox[{{3.266032535102632, 0.5176561427471635}, {3.338240507500868,
0.5256379589074991}, {3.345156080957054, 0.5264049285112669}}]}},
{GrayLevel[0],
{Arrowheads[{{0.06250000000000001, 1.}}], ArrowBox[CompressedData["
1:eJwBgQF+/iFib1JlAgAAABcAAAACAAAAwkxTrSZvAECYm8K38vX0P8dV2tfl
LwBAOfDtL5ps9D8ZxAvUTuv/P6SQhCNf5/M/pMlIaVt//z/lpSGd+mPzP+7r
VkFcxv4/AFxspvZk8j8MXhp+dmj+P+Tah9B9wvE/2+mqCHEo/j+pP3R9dijx
PzChlV+mC/4/advT/dmA8D+eayNfWjP+P22Bqq2R1u8/XO6G3wO//j/74lcH
YtzuP+SkyYuzVf8/EhDjowll7j+u46YCMxsAQKM2Tu95De4/a2WBYsDBAEAJ
3YGZE+LtP9AqHtUMUgFAmdGVuGDl7T8qHSzoE6oBQCtF2ekP8+0/cXIx8kEP
AkCdmuMJiwruPxSgWu74hAJAA4WpGiIu7j+CG9TXmg4DQHG3Hx4lYO4/LWLg
I8KuA0CsP992nKLuP9odo1AOCgRAgLYYk8LL7j/rMgMVMm4EQElSXD8Y++4/
BELz17vcBEBMFEVtpTHvP1+dUyYv+gRAKsxIqb5A7z9YFLNk
"]]},
{Arrowheads[{{0.036392079903049504`, 1.}}],
ArrowBox[{{2.696575561347587, 0.9862509414915123}, {
2.7303206592881617`, 0.9906456046081507}, {2.8, 1.}, {
2.861113223855402, 1.0085902487418705`}, {2.928496695738482,
1.0182311649251208`}, {2.9997082913096524`, 1.0285075165182915`}, {
3.0785761342570055`, 1.0400547389313033`}, {3.121274995686638,
1.046367580210606}, {3.1666756133400926`, 1.0531234462255825`}, {
3.2147779872173685`, 1.0603223369762327`}, {3.2655821173184663`,
1.067964252462556}, {3.3197636270333857`, 1.0761555905753593`}, {
3.345156080957054, 1.0800132869375652`}}]}},
{GrayLevel[0],
{Arrowheads[{{0.045736566519452494`, 1.}}],
ArrowBox[{{2.545010331856672, 1.6142829472439577`}, {
2.5653088085805047`, 1.5975930374724425`}, {2.611331640526089,
1.5887263475124795`}, {2.6584664880757574`, 1.5890798827431052`}, {
2.7272112547048684`, 1.5962322321118507`}, {2.7728920447604652`,
1.6033499105528897`}, {2.828439979025207, 1.6135397243095784`}, {
2.8945857043880734`, 1.6271129394298347`}, {2.9331813831570592`,
1.6355820315150855`}, {2.9761554221450917`, 1.645374291564695}, {
3.0243206971815546`, 1.6567209124429825`}, {3.0784900840958316`,
1.6698530870142678`}, {3.135661526949016, 1.683878038432052}, {3.2,
1.7}, {3.2475409307646834`, 1.7122519450203786`}, {3.299541633383827,
1.725777455280372}, {3.345156080957054, 1.7376896595812654`}}]}}}},
GraphicsComplexBox[CompressedData["
1:eJxl2Hk0lG/YB/AxZsaYZIk2VESl1fIjFK67IlEJJSVKWdJmz1ZZS7KTspQW
pChCSmV5ZN+y7yVrdhr72F/vec8888frH+dzHIfzzP1c9/X9il6x0jUjEgiE
LjYC4X+//9+XdpaR0vL8BXcOxLS2M7Q767I8W6Opp4RRcA9z+ykYhLDcfrxc
yMmE5UdxjSEHqsm473auu30uhmWrzfrnHOxZXu94pVKhk4Sblh6TevYTy4v0
rjD7ByzHa4zS5MfZcUd67xs9U8Cyf75lje1TluWEXdTl2FmWOP991+kGIm6h
p3Orbd6ynD9Kvv+fAMtfdh+9qtPLhjvBwlvT6ivLOj9CcqW3say6VBN7aoaA
W/7gmoe3SlnueLxpUXI/y3XVRh0nqSz7Cyk9bEpfBqZ/V+jaGQYu4c4/WqcY
IcNyYu5pQn3jIu45m+vD51IWcHcMDaaFnWG5yOyGczVjHve69Z5merVzuBeD
iXtCHFjuoXmNVwiyLJsV+UdnkoFbcL/gm4AIlgkpUTdKlVjWvpyqr7VuBrf8
L+nNvt+ncW/WS+spvMiyJaW0WlNhCvcZd41w79+TuA/MlRrlubPs+75DQ91g
ArfNtsu8XkvjuM+97GzMiWH5nTYj78jdMdyBZU6P3ERYtledPZVZQMf9aGiL
k7vSP9xn20XIjPujuMXqREOtfo6wPh+5U9ed3YdwB+/UnqGXDOI22qRz34KP
5UU3V0Pbgj7cZXZuAwNcLIdfdXe4rNfLen5lSVo3qD24STnJv7q0u3HXpH60
MIjsYj0PgTZkeqID913erGcZO9tZnz8j+3P89zbc+tkbzL+LtOAeixN0T0ht
wu3nLxwVcbgRdyjHsXOfTBtw7/mnYRszVcc6b43H/UO8a3FrhF0eerGeaQLh
p46j5od3Nbi775iQA99V4zZXdDZ9pshy3cimhzpPqnAvH5peEHjyE7frVaHE
5q8VcFXONFx95yrUXJTJI3abHeXJ28x3LtJQh5U9V/0JdjR5K94rqIiGCrDV
mkqb2FGWkusrxQc01DzK/Xd7MxFtyrvfI+FJQ8x54Wc6MFzgREP8GR1mqIKI
pCpLnKYO0tC3xGczUo+JqDi7aWM4kYasDhM0ao2IiFc1ImF3JydqbXxoqKtM
REM1DVUdCZyoZ3FAN4KbiFK09n5z9uJEzPlidjwtbZMyJ0p4+LX7eAwbIlEd
uhWFOdGAwbq6Qm821PVmt6I6mRMtCvg/qLZkQ991KzJ5IqmIbvs5vYXChgpm
iWsEgqjI40qW+pMlAqodJAsI+FARcx79aDLfGaRLRX9GNU0m8wlou0XGedtj
VLReYb784XcCik3MTO+gUpF/3/q8SjcCKicRFIwIVMRtzt/m40hA3Aa9BWxT
HOhChxJn1E0C6rywm0PahwMx59dPv1umWZYcKAPz+ij/dxlMLhMqJ7Q50FNp
3Ry3+GV41dabpkXlQLL26ouRosvwcKfX4dk2CuKWGk4QbF2CrxaCTX8/UJCe
OCNaxm4JGLxtcPwRBTHn3YZLzqtf66zcM9yPKYEli+Dzak1C8xoKuh17THan
7iK0BM3w9dIoSHfjJYenRxaBy1q2o4lKQcNr8idiYRE69ar0HX+QkVDltbsh
WQswcu/NOW0fMmLOR2NHrYFSUzLS0K7ur+FdAI2HOj0BUmSkbyGu+SF1Hty2
PzK9TCEjyxyHf6Fm8/DZ1WI8M5eEfpvG3E7rnAN1Dc2tvS9JqEGQfuVq/BwE
7Ul1375ybzHnKc3bcz5JmITs0+q/nkibBReTDVu9eEhI7+ga7ZyoWXgfWZqY
TCIhf5NAi6CHs/Dfnr83bhazo55aXyxPYBbmyz+2Z31kRxprtrk09zNAkZ3n
saIXO2LO39Rfm5M0XNkRr1ruh5PBDLgY8Jz0yokd/R4vJty7z4CDUKNStURE
76jxnX4JM9DoJXGCMkREFXxnrjX4zEBa2JfVofVEpBk/3StvMAN0M1WhThci
Ys5rtg3ZxPMGRLTj3+7giHvTwPG8et19KSKKevbChVdqGoqnCw85zrChoqRs
A5/yKRANmiB9LVg5x7vGI0Odp8AwdnCLgz8bunM83USQMgVRzuLJUfZsiDnf
s17pvH8nzYbSbEcfVdpMwo5WzcVSOgF16TbU3R+ZgJRE0k6LfgLiSbMxGWyb
gJAS+t43LwgoMMtZZvbaBHAwAs48vkZAzPlPStssY6BKQGTR2MFf38bB79iG
G0o8BGSueSSw23AcjG7o34rvWYb3adOtzdvGoVBggWtN+cq9yxg+4cEzDkGb
dKlevssgWn/KLKFlDKKCDtvJqy2DeqfMDULEGNhotwVKHFmGIKVQ161PxyDN
1sYhAi2Dh7jZ29rHY2C4WtJoiLEE//YqpH8+MwblhQUxJ7OXgHnfcLj4ufk+
X4J7h6rKONjHoEbz01G3K0tgPfUg8WgdHYz2e9Ks5Jag4VPO26V3dDD0eONz
l7EIp+N5fO/Y0mELW8XpW5WL8Lh9gU1Umw4HItjpYomLIBxNKronTQdycEuU
8coe4PpLXlTmzSjUvYoaNHizAP370tooT0ZBbMn39tboBWDeZ1dtTMtSVRdA
Xyji9br+EQg4dSNgK98CeOjRvSYCR6Ce91HxnUfzYHdfwXUyfhj+ux25/Mll
Ht4v61I3+g9D8ovVSaoW8yB6jHhx8fowrIOfgly2c8C8/8hH0gsvnpwDw6oL
vPwPB0E/6RAmITIHHzruif7aPwjfsvhILednIanyqvXIYD+kuwS9PbFlFjY1
GWuIePUDIet2DVczAyRH8kQvUfrBc5/fFfpDBlwibxd55dEHVvHJlomIAcz7
07FSbrUefQbeu+1suuPeCwllCd30oBkYNLukKt76FwTHvG4e2D4DfRvCr/Tu
+wu3ZOh/j+ZOQ6n9Brlbbj2g29I2Va8+DcLTvArtad3wdUe5hDRtGpj3rWBZ
5uPewClwsmNXOe7eBfN9fNRvy5MwJMWtZxLSCRtL/5ptGZ4EUZOiM+22ncAW
Tk/zujQJAX2eq50edYDU81uZnRcmIYffdiTAqwO0/+3me79iNdmer7tX3EVq
dT9XMgHM+/oN3fWLTO4EMFp/66bztkPctJpgdMbKe1CRa7pu/A+4q+iQiv+b
gMjPdQLpx9tAdJfKXLL4BBwVvP+hcmMbMBYviQXxT0BvC636SedvqCd5Nh97
MQ5fDIYCUm79grgIK9FDD8dheYm27p7ELzhJdtnjYTUOolZcZlsaWmGX5g6x
fI5xqF8mciQFtcD+lxKCskNjcDr4pPOO/1oghitMzq58DESNz84SfzbD0mCf
23rrMWDuD8+zpCXaj48BmxbX7svqTTDNn6xitmMMFF2ENoWXNkKROf2mWBMd
uDVlZt/UNYDP20GDzUkr5/5akdzQ+QbQFCpR1/eiw+9UhTzF8npQMZOLwpTo
wNw3SvSODQSvpkPJKPlhqWUdqKgVvA7N+Qe7rLuntGtr4c6pdAnXQ/+AuX+c
SBT3VWsdBX2tl4H7vWug7zTjk4PDKEwlX/x4vL0a2qft7v8mjwJz/5Dk4xG5
Ez4CeTc7x3tRFQRf2VNksG8EjNP/3FT7+xNm3Tt0xYqGgZItmimZUQGYcd/M
H/1h4FTIURa+WQ6KNsbNKr1DUFVhqPFpYxmkMi41lHgMAeLQSZKYL4HNtilV
J1cNwQm1UOs12cXQ5RY2uPXFICj4PKMRjIogJLstf4/CILjouL8UhUIQdi2M
nCsaAMf4xBLSdD74BZYsUM4OQN739n1mKXlwfTr+5eP+lffo2ccQQa8foKr1
qzDTvh98S/dEe+vngmz0AvfQ6n4okj3ZbrsrBzZMWNWIhPbB7/Jsjh2BmWCq
wKHRIN4Hux/stTA3/QZt76VEqwp7IT5Zo61vYwbIHvGXrvqvF3SMhYc3rEuH
8X+TNmY1f0FdNcb7wr408P5u+t+ne3/Bd1Iv9JJMCsR9nLO/WtEDfgNTr9Yq
JUC1qmIeyaUHerKLTYI2x4NkaYRauFwP2J4c9MwdjQHfToNCO4Nu6Bc3rxsP
D4MILJtLeXM3UA6R9S13BENzU4X+nZEu0G/VfqVp/hA2dzbflfzdCf5rYL9f
sCeWuiqyfCmnE2IoP27zHXyIefQSrl960wkCM9KRazT8MEaISXL2qk4oO62t
fnZ3JMa4d3PeM6oDfsdf9zMve4XtmpK9e8Ro5T0tS8ihssViaRnPZ7z1OmD0
HPd6gQOx2MFPPFIHV/bq789qSRAWi8Vz1Aqf2vUHKm/WTcTeS8Y+kl4WHc9v
A2s4sZOyLgXrf8ufMi3dBhbfaC/2Hk7FGOIHDq2P+gXb1ZQ65NLSsZua4+tl
v7ZCKe1Mz2qJL5hrcHsMV2gLTIp/+Hbw+1dM83CMWTtnC6zll1a1rPuGOba6
P/0y0QRGsYa6X3sysaQ/nV9cPzcB7ZXqNS/dLOz5JZrvW+dGmJvnEQtxzMGi
w9Y8EbnUAKgkflB8Yy7WJOn4Scu6HgTCnOxi2nKx0bu2yVYDdTDX+YSzUfMH
5h5OC+LKrQUrzmSXQbE8zFaFc9Wvo7VQtrYsZdolD0NRrbXy52tA5vX5HhJv
PuYl2Wp3caIairm19ctQPjbwjvuvEF81OJCTXKMr8rHZuWR9gcUqoLg6MnY3
5GPGOrxXIkQrIdt27dtC5QJsm9WD0eWQn+BwZzuH2tUCbNn9zdOTjhVw1Mhe
cWNsARZepF/5fW8FfHU21Ej8WIA5+Y+sKWErB6+JhIPkrgIsdNc2Aa01ZWC2
/8RINqkQEx7s6iTtL4XXw1K2AuKFWFmCnnywTQnYNr6yiNpfiJ3eUhXxuqEY
MilVGpGHCrGTz6XOtp0vgnnqBKfZhZXfL86+cK6zEI6Z3fpTYViIycwYrAu3
KATxnuDNiis/D+noD/WozQf5Kznt9DOFmGXPNncRnXzgTOa+ZqpZiAVcIwve
eJcHqUfImZoKhZiEocZa1cc/QMhRXnByYyGWyxYY15+bCxeKLm4KGy/AzvnM
TuwRx0BjXIAtL7UAK9EJ21p2OwcWJhoz1oavPB+V4ZDLl7PAiRZ34D+1Aux7
iCP5clAmbDLSCn4nWoCt5w8RLZD7jj/fMqes1jGUAatvGW9+ujUfkwi53T3m
+Bkinn7b8Cw6D5vfs+2cbuInEBMLspGY+YFZfvIX8xRJg7tb92O9F39gS/Zz
QnmBKWBdHbfW6X0ulhaXUeZ97CN+fvYonqCOyiTAJG/XP8KPLIwQMUS1H3sL
jIBbEpZfMrF4/uB1yXvi8PN7nYZao37FQBd3Wbh0RAbWHJNe7+v6EvgOrJ8V
25eOvZJzUz5XHIW/H1zmVd9KPj0G0Y/X6Jntb7GCV5XTCaUh+PuWRz158+/Z
ANA6v/3Kqr4ozMBExaWA2w/u18eZO118iomoU83u/vHG50FuUofXnxIPcF43
pPPwvjU4/JHsbSd6gD0fW+Tr1nvgH/jypDzPXXze3DXoiUuuvA1Pdofp7imJ
BYUZr1O9Qtb4/LI+yks4IXUN+tqFfZRbkiD3vwz30z+N8XmIznQvXeTXB9Hr
F4a2BH2DDttyxQp+NbgVZuMXb5EN7ukR4vtK5PD5TKh9KmoSuwcUp7wQ2bAA
CEP7n6sarYWC0qKEo7KFQFBYhOuTsyoZpTyjbRxFQOg4sF1W+5/K8y+FZ0zt
imC/cX2Dv90YxszBzUXzTo5Eliv27kqufzeKm3feaTKhaAT3mZLiA249w7it
LeamTX0GcKfLaSgfiO/HzSBGePEU9OEWiC2Dqas9uM9Zb/Que9CN+7myRcXL
2C7cNplyfKuC/uCe1auL/lz2G7cH3XqXMeUX7kypxpjdWvW4D5fbSTY+qsVd
asaX5V5YjZtyYsQiQrCA9f95SHiOhOTiVrtZvP/Bmu+4bVvETimoJuDmOlS3
hbcpBjfeJ3gdDkgYoyCuIdWPX7atQtMvGzvnBimIPbvri6LQKnTL7ug9/SYK
olZdPF6xdhU6JmiRIPiTggaSdsR7c65C92LzlGY/U5A0pxN2nrQKJeok5qKV
3EumdUTmT9EQs19VqpnlPzdCQ9WafCGHPShojeLYM9REQ5dc4j1q9Clo7Fj8
vyuNNCRKQocOnqWgauVsoloDDaW25FIkzlBQsudR0/efaUiWUX22ZSMFuX0t
Uh97S0PmlQXKQQQK3ne0vnbHMjAyktQIYuu0pyFmX2tx43zSXk0aunnwS0Sr
HhmV8flb/lngRKrPW9q9ikmoIMy5SmOMEzH72moQECGMcKK4WIH4r4kkvP9o
f7Wn813YihNpecnJnEg3ur+q4SAJBV3ov3YhgBOtV1vrcIVtJQfnBkoG3+BE
zD6X2Yd4y6z98MGaHd3Z0Byjt2/l70ULuEfosyP3f6HrRDdyIqm6QOVoGXYU
UScsT++i4n2NhLZC93AFFaWd7w33+0hEpqRH+WkvqHg/w+xPrPpu9XedJqIn
73x+S9ygIoa2xN4fHERkR3mz/FSfivczYb4+xKTtVHQgt75oKZQNuV12LHpL
pSK/2tMu7sZsyF/68CPHQg68b1F+7LzlbywHYnAvuvV8J6AGW303N3cOvF9h
9iOF/O9OJksRkER9la8ucCB2xmGPbWsJKPHihlP68qx+xZunQZW2lQOtXSw1
OlKxDHzBvEbqzRTE/SIzxryL1Z8IORzWZNdbAiwwt+j1a1Z/QlvkqpGxpiDB
org/pOeLoPPYYSv5zP/vS4Yq/CkXzi2AIzn8zjwHBYXAh5IGvQXQruWnhayY
2Ze84csjXqRQ0KHyNKVZ7QX4vKQ8LPKcjKbPJhlPCMzDY3LJzt4rZLz/+BYo
ebtCkozG7c1C8+pn4XfRDc/JIhKy4uGoin7NADAns9fnk/A+Q4tfyK8sj4Tk
nmK3A58w8L7l7Z47dpZBDHAebnvKZknC+4zX5+2o8zokJFx69kfPhRm8b0n6
GL3pa/40yL+Z2nRgIwnvMxSVEx+odbCji73dor5i0yA9a/uSO5cd7y+Y/Ylv
zaVr/6hTcGN6l8W9W+xou0dTKLaS62YFKafVrrLj/YV/Q+yXvTrsSIS37xV3
7CQ45Ssckp4hoqgsm0MCmRNQxeju8HlHxPuJnn5UmOVKRNjh/OgA/3FIOfba
5NBJImL2D8x+RbvLVZG/eAxUA0R3BJKIyMJKUNjPeAxCiGdFBgbYELNPYPYr
1fct+1wQHbLmhm2MfdiQmHKIjI08HXiMO/0andlQPG8s0XAdHdrPKSfzCbMh
Zv7ni54ML+FgQ9eN3Lz9do7ifUtrzvi/nyu5p7Jj/a8tKQTEzP+nHLdKm98n
oPpt0x/ODg/hfQu7gYZkVO0g3OVkCE8fIiBm/j8SOSuIFpbBav0ppYCMAWgw
0p3LjFzG8z6zPxGJPhCKZPphs/mtFtGBJXgmUKZ41r8PJmJNPBlvl/B8z+xD
6gRNvjz78hdUCF8UgyoXoar3r+P8jb+wJXFfslrSIp7vmX2I3bGU/dOXukH8
ogXF//0C8L45Zz6s3w1WbQfW2r5dwPO9mM6ddnP7BchvLTPznO2CY1oz8ffu
zYO3xrtdk6c7oU9S65mdyRyezw8ePov41OZgS2gn596cP3i/YVTctAmp/QER
O68S6V2zeN5Ogwf6V9hmIXLhTjyaasX7jRena97bOLZCh0jVWr/6GTw/G9Zu
cNicOgPmG1YZLWo34X1GkJFz0NOJRujbZaD2/NI0nocNhQM6G3WnwSQ0LjOo
oQ4+TjRdvdczBa2fbdX31tfifcUfrqoLh4ur4XS1FJWnexLWd8reEQmohpdX
WvLXZk7i+ZfZNwRnXXnGplgBB0ZiTnIbT8A+HfEO89kyMD6SIVDYPI7nWWZ/
sG5IhOu3ZTHMj9AJbSVjEHx94aWsViGe/xPelsuG7skHMHt9bNUTOr4P5fpG
7v4iRIevPb0ts1tz8TwfL+rCz/0rByzXbFE/7jQKd522xddEZEJzTwLHfNww
RJU874zbnwHmu7284uWH8H2MmacjlPc+3F2UBvsGslUUGvqB28Bz89mNH0Fi
KnOLWEIvXLc73jMw8hbPr/s2t4UH2ccB6Ve+lkBBD3B3cwxfxmLw/Cm1ocUn
3uU5qMcympIbOvD9UXHbMR42yw4YUFLZ/J3vMTDz5JFAvsKEqlC4qz9h3360
A5q77DTJgaHQdSPl88anTUDScrowEuoKzPzGq1c08XrcGapT1XkNpRqglufB
Bn4LB1BtyMsgJpRDinVzylyYETDzjbtp6wlN2dOweyHk6X6eQnDn6vtoPXAc
vjMkL06VJ4H73tSbpuwiwNy/CceOCN3OH1O53eShdCjhKkYw7vkxzP5G5X8A
Up9fYg==
"], {{}, {},
TagBox[
TooltipBox[
{RGBColor[1, 0, 0], Thickness[0.01],
LineBox[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51,
52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68,
69, 70, 71, 72, 73, 74, 75, 76, 77, 78}], LineBox[CompressedData["
1:eJwl0uN2kAEAANBv2baXbeMZqmXXsrZs29yybdu2bdu27jn9uG9wQ8MjwyJC
giB4S2WqUJUwqlGdGtSkFrWpQ13qUZ8GNKQRjWlCOE1pRnNa0JJWtKYNbWlH
eyKIpAMd6URnutCVbnSnBz3pRW/60Jd+9GcAAxnEYIYwlGEMZwQjGcVoxjCW
cYxnAhOZxGSiiGYKU5nGdGYwk1nMZg5zmcd8FrCQRSxmCUtZxnJWsJJVrGYN
a1nHejawkU1sZgtb2cZ2drCTXexmD3vZx34OcJBDHOYIRznGcU5wklOc5gxn
Ocd5LnCRS1zmCle5xnVucJNb3OYOd7nHfR7wkEc85glPecZzXvCSV7zmTfD/
4Dve84GPfOIzX/jKN77zg5/84jd/+EsgcwgxiEksYhOHuMQjPglISCISk4Sk
JCM5KUhJKlKThrSkIz0ZyEgmMpOFrGQjlOzkICe5yE0e8pKP/BSgIIUoTBGK
UozilKAkpShNGcpSjvJUoCKV+AfBB327
"]]},
RowBox[{
RowBox[{
RowBox[{"-", "x"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"0.2`", "\[VeryThinSpace]"}], "+",
RowBox[{"1.1`", " ", "x"}], "-", "y"}], ")"}], "3"], " ",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"0.2`", "\[VeryThinSpace]"}], "+",
RowBox[{"1.1`", " ", "x"}], "-", "y"}], "]"}]}]}],
"\[Equal]", "0"}]],
Annotation[#, -$CellContext`x + (0.2 +
1.1 $CellContext`x - $CellContext`y)^3
HeavisideTheta[0.2 + 1.1 $CellContext`x - $CellContext`y] == 0,
"Tooltip"]& ],
TagBox[
TooltipBox[
{RGBColor[0, 0, 1], Thickness[0.01],
LineBox[{318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329,
330, 331, 332, 333, 334, 335, 336, 337, 338, 339}],
LineBox[CompressedData["
1:eJwVzec2FgAAgOHPpbiljmSECAllKzsjKyV7Nih7K4qG0SBbVhHRlfT48Zzz
/nuD49Ku3A0KBAL1hIirhHKNMMKJIJLrRBFNDDeIJY6bxJNAIrdI4jbJpJDK
HS6HaaSTQSZZZJNDLve4Tx75FFBIEcWU8IBSyiingodUUkU1NdTyiDoe84R6
ntJAI00000IrbbTTQSdddPOM57zgJT308orX9NHPAIMMMcwIo4wxzgSTTDHN
G94ywyzveM8c83zgI5/4zAKLLLHMF77yje+ssMoP1lhng0222GaHXX6yxz4H
HHLEL35zzAl/OOWMv5xzwT/+A0/aWWc=
"]]},
RowBox[{
RowBox[{
RowBox[{"-", "y"}], "+",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"0.01`", "\[VeryThinSpace]"}], "+",
RowBox[{"0.5`", " ", "x"}], "-",
RowBox[{"0.1`", " ", "y"}]}], ")"}], "3"], " ",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"0.01`", "\[VeryThinSpace]"}], "+",
RowBox[{"0.5`", " ", "x"}], "-",
RowBox[{"0.1`", " ", "y"}]}], "]"}]}]}], "\[Equal]", "0"}]],
Annotation[#, -$CellContext`y + (0.01 + 0.5 $CellContext`x -
0.1 $CellContext`y)^3
HeavisideTheta[0.01 + 0.5 $CellContext`x - 0.1 $CellContext`y] == 0,
"Tooltip"]& ]}]},
AspectRatio->1,
DisplayFunction->Identity,
Epilog->{
PointSize[0.05],
PointBox[{{0.009289517143394582, 3.140643980082845*^-6}, {
0.6250503995994064, 0.032544484944664095`}, {2.845156080957054,
1.912675446249655}}, VertexColors -> {
GrayLevel[0],
RGBColor[0, 0, 1],
RGBColor[1, 0, 0]}]},
Frame->True,
FrameTicks->{{None, None}, {None, None}},
GridLines->{{{0.009289517143394582,
GrayLevel[0]}, {0.6250503995994064,
RGBColor[0, 0, 1]}, {2.845156080957054,
RGBColor[1, 0, 0]}}, {{3.140643980082845*^-6,
GrayLevel[0]}, {0.032544484944664095`,
RGBColor[0, 0, 1]}, {1.912675446249655,
RGBColor[1, 0, 0]}}},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
Method->{
"DefaultBoundaryStyle" -> Automatic, "TransparentPolygonMesh" -> True},
PlotRange->{{-1.0737285140752095`,
3.4281741121756584`}, {-0.3830148905746239, 2.9956934774682593`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.05],
Scaled[0.05]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{
3.691134202135131*^9, {3.691134482072929*^9, 3.691134493232272*^9}, {
3.691135464444171*^9, 3.691135521071075*^9}, 3.69113555156861*^9,
3.69113558514855*^9, {3.691135669538349*^9, 3.691135811321965*^9}, {
3.691217397332892*^9, 3.6912175960938053`*^9}, {3.691420380059111*^9,
3.6914204165766563`*^9}, {3.6914204541994457`*^9, 3.691420561018105*^9}, {
3.691421852758523*^9, 3.691421893486292*^9}, {3.69142205105159*^9,
3.691422182787798*^9}, {3.691422217228775*^9, 3.69142235850133*^9},
3.6914224825225058`*^9, {3.691422513992503*^9, 3.691422606012048*^9},
3.691422640697515*^9, 3.6936400219527483`*^9, 3.693655825640711*^9, {
3.6936558663135967`*^9, 3.69365588348368*^9}, 3.6936563248986597`*^9,
3.6936565414858*^9, 3.6936565785533524`*^9, 3.693656612856802*^9, {
3.693656719623467*^9, 3.693656748824079*^9}, {3.693659939167927*^9,
3.693659947413575*^9}, 3.693660067741686*^9, 3.6936601360451717`*^9, {
3.699293797371296*^9, 3.699293815907547*^9}, 3.7099972335798903`*^9,
3.709997322525209*^9, 3.7108216871124973`*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{"Figure", " ", "2",
RowBox[{"(", "D", ")"}]}], ",", " ",
RowBox[{"four", " ", "steady", " ", "states"}]}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Clear", "[",
RowBox[{
"Jee", ",", "Jei", ",", "Jie", ",", "Jii", ",", "ge", ",", "gi", ",", "n",
",", "te", ",", "ti", ",", "cminus", ",", "F", ",", "P", ",", "Z", ",",
"z0", ",", "Z", ",", "re1", ",", "ri1", ",", "re2", ",", "ri2", ",",
"re3", ",", "ri3", ",", "re4", ",", "ri4", ",", "plot1", ",", "plot2",
",", "plot3", ",", "plot4", ",", "Ge", ",", "Gi"}], "]"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{"**", "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "**"}],
"**"}], "**"}], "**"}], "**"}], "**"}], "**"}], "********)"}],
"\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{"SSN", " ", "parameters"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**", "**",
"**", "**", "**", "**", "**", "**", "**", "**", "**"}], "********)"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jee", "=", "2.25"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jei", "=", "44.4"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jie", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Jii", "=", "20"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"n", "=", "3"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"ge", "=", "0.2808"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"gi", "=", "0.015"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"te", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ti", "=", "1"}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"detJ", "=",
RowBox[{
RowBox[{
RowBox[{"-", "Jee"}], "*", "Jii"}], "+",
RowBox[{"Jei", "*", "Jie"}]}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"cminus", "=",
RowBox[{
RowBox[{
RowBox[{"-",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}], "*", "Jee", "*", "gi"}], "+",
"ge"}]}], ";"}],
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
RowBox[{"Characteristic", " ", "function", " ", "for", " ", "detJ"}],
"<", "0"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"P", "[", "z_", "]"}], "=",
RowBox[{
RowBox[{
RowBox[{"-", "detJ"}], "*",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"z", "^", "n"}], ",",
RowBox[{"z", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"z", "\[LessEqual]", "0"}]}], "}"}]}], "}"}], "]"}]}],
"+",
RowBox[{
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jee", "*", "z"}], "+",
"cminus"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"F", "[", "z_", "]"}], "=",
RowBox[{
RowBox[{"Jie", "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"P", "[", "z", "]"}], ")"}], "^", "n"}], ",",
RowBox[{
RowBox[{"P", "[", "z", "]"}], ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{
RowBox[{"P", "[", "z", "]"}], "\[LessEqual]", "0"}]}], "}"}]}],
"}"}], "]"}]}], "-",
RowBox[{"Jii", "*",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"z", "^", "n"}], ",",
RowBox[{"z", ">", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",",
RowBox[{"z", "\[LessEqual]", "0"}]}], "}"}]}], "}"}], "]"}]}],
"-", "z", "+", "gi"}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"plot1", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"P", "[", "z", "]"}], ",",
RowBox[{"{",
RowBox[{"z", ",",
RowBox[{"-", "0.2"}], ",", ".1"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<z\>\"", ",", "\"\<P(z)\>\""}], "}"}]}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"Directive", "[",
RowBox[{"Blue", ",", "Bold", ",",
RowBox[{"FontFamily", "\[Rule]", "\"\<Helvetica\>\""}]}], "]"}]}]}],
RowBox[{"(*",
RowBox[{",",
RowBox[{"Ticks", "\[Rule]", "None"}]}], "*)"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot2", "=",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"F", "[", "z", "]"}], ",",
RowBox[{"{",
RowBox[{"z", ",",
RowBox[{"-", "0.01"}], ",", ".47"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<z\>\"", ",", "\"\<F(z)\>\""}], "}"}]}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"Directive", "[",
RowBox[{"Blue", ",", "Bold", ",",
RowBox[{"FontFamily", "\[Rule]", "\"\<Helvetica\>\""}]}], "]"}]}]}],
RowBox[{"(*",
RowBox[{",",
RowBox[{"Ticks", "\[Rule]", "None"}]}], "*)"}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{"GraphicsRow", "[",
RowBox[{"{",
RowBox[{"plot1", ",", "plot2"}], "}"}], "]"}], "\[IndentingNewLine]",
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<detJ=\>\"", ",", "detJ"}], "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"z0", "=",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{"P", "[", "z", "]"}], "\[Equal]", "0"}], ",", "z"}], "]"}]}],
";"}],
RowBox[{"(*",
RowBox[{"Zero", " ", "crossing", " ", "of", " ", "P"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<The zero crossing of P is z0=\>\"", ",", " ",
RowBox[{"z", "/.",
RowBox[{"z0", "[",
RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Z", "=",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{
RowBox[{"F", "[", "z", "]"}], "\[Equal]", "0"}], ",", "z"}], "]"}]}],
";"}],
RowBox[{"(*",
RowBox[{"Zero", " ", "crossings", " ", "of", " ", "F"}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{"\"\<Four zero crossings of F are z1=\>\"", ",", " ",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ",", "\"\<, z2=\>\"", ",",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ",", "\"\<, z3=\>\"", ",",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "3", "]"}], "]"}]}], ",", " ", "\"\<, z4=\>\"", ",",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "4", "]"}], "]"}]}]}], "]"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"Four", " ", "steady", " ", "states", " ", "in", " ", "the", " ", "phase",
" ", "plane"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re1", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "detJ"}], "*",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jee", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}]}], "+", "cminus"}], ")"}],
"^", "n"}]}], ";"}], " ",
RowBox[{"(*",
RowBox[{"steady", " ", "states"}], "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ri1", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re2", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "detJ"}], "*",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jee", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}]}], "+", "cminus"}], ")"}],
"^", "n"}]}], ";"}], " ", "\[IndentingNewLine]",
RowBox[{
RowBox[{"ri2", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re3", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "detJ"}], "*",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "3", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jee", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "3", "]"}], "]"}]}], ")"}]}], "+", "cminus"}], ")"}],
"^", "n"}]}], ";"}], " ",
RowBox[{"(*",
RowBox[{"steady", " ", "states"}], "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"ri3", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "3", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"re4", "=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-", "detJ"}], "*",
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "4", "]"}], "]"}]}], ")"}], "^", "n"}]}], "+",
RowBox[{
RowBox[{"Jie", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}], "*", "Jee", "*",
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "4", "]"}], "]"}]}], ")"}]}], "+", "cminus"}], ")"}],
"^", "n"}]}], ";"}], " ", "\[IndentingNewLine]",
RowBox[{
RowBox[{"ri4", "=",
RowBox[{
RowBox[{"(",
RowBox[{"z", "/.",
RowBox[{"Z", "[",
RowBox[{"[", "4", "]"}], "]"}]}], ")"}], "^", "n"}]}], ";"}],
"\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"Print", "[",
RowBox[{
"\"\<Four steady states of the SSN are re1=\>\"", ",", " ", "re1", ",",
" ", "\"\<, ri1=\>\"", ",", " ", "ri1", ",", "\"\<; re2=\>\"", ",",
" ", "re2", ",", " ", "\"\<, ri2=\>\"", ",", " ", "ri2", ",",
"\"\<; re3=\>\"", ",", " ", "re3", ",", " ", "\"\<, ri3=\>\"", ",",
" ", "ri3", ",", "\"\<; re4=\>\"", ",", " ", "re4", ",", " ",
"\"\<, ri4=\>\"", ",", " ", "ri4"}], "]"}], "\[IndentingNewLine]",
RowBox[{
"(*", "******************************************************************************************************)"}\
], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"Right", " ", "side", " ", "of", " ", "the", " ", "SSN", " ",
"equations"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{"++",
RowBox[{
"++", "++"}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}]}],
"*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "x"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Jee", "*", "x"}], "-",
RowBox[{"Jei", "*", "y"}], "+", "ge"}], ")"}], "^", "n"}], "*",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"Jee", "*", "x"}], "-",
RowBox[{"Jei", "*", "y"}], "+", "ge"}], "]"}]}]}], ")"}], "*",
RowBox[{"te", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Gi", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "y"}], "+",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Jie", "*", "x"}], "-",
RowBox[{"Jii", "*", "y"}], "+", "gi"}], ")"}], "^", "n"}], "*",
RowBox[{"HeavisideTheta", "[",
RowBox[{
RowBox[{"Jie", "*", "x"}], "-",
RowBox[{"Jii", "*", "y"}], "+", "gi"}], "]"}]}]}], ")"}], "*",
RowBox[{"ti", "^",
RowBox[{"(",
RowBox[{"-", "1"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{"Clear", "[",
RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}],
RowBox[{"(*",
RowBox[{
"Define", " ", "the", " ", "plot", " ", "region", " ", "around", " ",
"the", " ", "steady", " ", "states"}], "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"a", "=",
RowBox[{"re1", "-", "0.4"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"b", "=",
RowBox[{"re4", "+", "0.2"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"c", "=",
RowBox[{"ri1", "-", "0.01"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"d", "=",
RowBox[{"ri4", "+", "0.01"}]}], ";"}], "\[IndentingNewLine]",
"\[IndentingNewLine]", "\[IndentingNewLine]",
RowBox[{
RowBox[{"plot3", "=",
RowBox[{"StreamPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x", ",", "y"}], "]"}], ",",
RowBox[{"Gi", "[",
RowBox[{"x", ",", "y"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "a", ",", "b"}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",", "c", ",", "d"}], "}"}], ",",
RowBox[{"PlotRange", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"a", ",", "b"}], "}"}], ",",
RowBox[{"{",
RowBox[{"c", ",", "d"}], "}"}]}], "}"}]}], ",",
RowBox[{"StreamStyle", "\[Rule]", "Black"}], ",",
RowBox[{"StreamScale", "\[Rule]", "0.25"}], ",",
RowBox[{"StreamPoints", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"-", "0.1"}], ",", "0.02"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.09", ",",
RowBox[{"-", "0.003"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"1.3", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1.4", ",", "0.051"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1.68", ",", "0.066"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1.5", ",", "0.068"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0.6", ",", "0.05"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1.1", ",", "0.01"}], "}"}]}], "}"}], ",", "Automatic",
",",
RowBox[{"Scaled", "[", "3", "]"}]}], "}"}]}], ",",
RowBox[{"Epilog", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"PointSize", "[", "0.04", "]"}], ",",
RowBox[{"Point", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"re1", ",", "ri1"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re2", ",", "ri2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re3", ",", "ri3"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re4", ",", "ri4"}], "}"}]}], "}"}], ",",
RowBox[{"VertexColors", "\[Rule]",
RowBox[{"{",
RowBox[{"Black", ",", "Blue", ",", "Black", ",", "Blue"}],
"}"}]}]}], "]"}]}], "}"}]}], ",",
RowBox[{"GridLines", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"re1", ",", "Black"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re2", ",", "Blue"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re3", ",", "Black"}], "}"}], ",",
RowBox[{"{",
RowBox[{"re4", ",", "Blue"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"ri1", ",", "Black"}], "}"}], ",",
RowBox[{"{",
RowBox[{"ri2", ",", "Blue"}], "}"}], ",",
RowBox[{"{",
RowBox[{"ri3", ",", "Black"}], "}"}], ",",
RowBox[{"{",
RowBox[{"ri4", ",", "Blue"}], "}"}]}], "}"}]}], "}"}]}], ",",
RowBox[{"FrameTicks", "\[Rule]", "None"}]}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{
RowBox[{"plot4", "=",
RowBox[{"ContourPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"Ge", "[",
RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "0"}], ",",
RowBox[{
RowBox[{"Gi", "[",
RowBox[{"x", ",", "y"}], "]"}], "\[Equal]", "0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",",
RowBox[{"a", "+", "0.05"}], ",",
RowBox[{"b", "+", ".05"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",",
RowBox[{"c", "-", ".03"}], ",",
RowBox[{"d", "-", ".005"}]}], "}"}], ",",
RowBox[{"ContourStyle", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"Dashed", ",", "Red", ",",
RowBox[{"Thickness", "[", "0.01", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"Blue", ",",
RowBox[{"Thickness", "[", "0.01", "]"}]}], "}"}]}], "}"}]}], ",",
RowBox[{"PlotPoints", "\[Rule]", "70"}]}], "]"}]}], ";"}],
"\[IndentingNewLine]",
RowBox[{"Show", "[", "plot3",
RowBox[{"(*",
RowBox[{",", "plot4"}], "*)"}], "]"}],
"\[IndentingNewLine]"}]}]], "Input",
CellChangeTimes->{{3.6911358675644007`*^9, 3.691135913500052*^9}, {
3.691135957329916*^9, 3.691136040823227*^9}, {3.691136074293722*^9,
3.691136263687315*^9}, {3.691136305911702*^9, 3.691136310018888*^9}, {
3.691136382278035*^9, 3.691136385205798*^9}, {3.691136430278532*^9,
3.691136535774536*^9}, {3.6911365671523542`*^9, 3.691136581975012*^9}, {
3.691136632493641*^9, 3.691136654836038*^9}, {3.691136739560648*^9,
3.69113676019704*^9}, {3.6911369974316072`*^9, 3.691137000816201*^9}, {
3.691139905616373*^9, 3.691139934759881*^9}, {3.6911399855398817`*^9,
3.691140019498363*^9}, {3.6911401450809307`*^9, 3.6911401593009*^9}, {
3.691140224738558*^9, 3.691140257442706*^9}, {3.6911403900121593`*^9,
3.691140430177924*^9}, {3.691140492835805*^9, 3.691140499628045*^9}, {
3.6911405319336977`*^9, 3.691140546918914*^9}, {3.691140656257016*^9,
3.691140738321991*^9}, {3.6911408191468153`*^9, 3.691140873370891*^9}, {
3.6911411018580103`*^9, 3.691141103165288*^9}, {3.6911411883111753`*^9,
3.691141205676386*^9}, {3.691141271217658*^9, 3.691141285968042*^9}, {
3.691141394791156*^9, 3.691141397097826*^9}, {3.6911414582794247`*^9,
3.69114146968287*^9}, {3.691141715510251*^9, 3.6911419275062437`*^9}, {
3.691141979268552*^9, 3.691141981582655*^9}, {3.691142028794959*^9,
3.691142061013648*^9}, {3.691142109262561*^9, 3.691142137249031*^9},
3.6911421936624928`*^9, {3.691142242418626*^9, 3.6911422424874077`*^9},
3.69114234833284*^9, {3.691142451441519*^9, 3.691142479566782*^9}, {
3.691142532597066*^9, 3.691142533080628*^9}, {3.6911425702934732`*^9,
3.6911425707123547`*^9}, {3.691142629835464*^9, 3.691142683275976*^9}, {
3.691142778770566*^9, 3.691142793356699*^9}, {3.691142894693461*^9,
3.69114289813595*^9}, {3.69114300871047*^9, 3.691143012893713*^9}, {
3.6911430475915203`*^9, 3.691143083251279*^9}, {3.69114313682513*^9,
3.691143186274118*^9}, {3.6911432482659817`*^9, 3.691143279254998*^9}, {
3.691143316437871*^9, 3.6911433432018423`*^9}, {3.6911434026219597`*^9,
3.691143496037944*^9}, 3.691143537324518*^9, {3.691143572605386*^9,
3.691143579021661*^9}, {3.6911436866658497`*^9, 3.691143725682547*^9}, {
3.6911438022366447`*^9, 3.691143804109909*^9}, {3.691143879468581*^9,
3.691143959617025*^9}, {3.691143994248273*^9, 3.6911442410276127`*^9}, {
3.691144714380389*^9, 3.691144748283929*^9}, 3.691144779572775*^9, {
3.691144861382547*^9, 3.691144874822188*^9}, {3.691144932613405*^9,
3.6911449421862392`*^9}, {3.6911451157966413`*^9, 3.69114531971826*^9}, {
3.691145375394833*^9, 3.691145395419697*^9}, {3.6911454556342573`*^9,
3.691145561230165*^9}, {3.6911456189382544`*^9, 3.6911458568428802`*^9}, {
3.691145887111516*^9, 3.6911464340900803`*^9}, {3.6911464752228317`*^9,
3.691146507436737*^9}, {3.69114653938057*^9, 3.6911469024468403`*^9}, {
3.6911469363607187`*^9, 3.691146942950198*^9}, {3.691146974016765*^9,
3.691147127637411*^9}, {3.6911471708580437`*^9, 3.691147181726233*^9}, {
3.691147299370863*^9, 3.691147342818994*^9}, {3.691147395964716*^9,
3.691147524008906*^9}, {3.691147558100671*^9, 3.691147658329587*^9}, {
3.6911476942505407`*^9, 3.691147718475828*^9}, {3.691147755294775*^9,
3.691147790749151*^9}, {3.691147846576589*^9, 3.691147855337035*^9}, {
3.6911479131901817`*^9, 3.691148257490713*^9}, {3.691148292812017*^9,
3.6911483170469112`*^9}, {3.691148350123891*^9, 3.691148518975398*^9}, {
3.6911485508807096`*^9, 3.691148553684218*^9}, {3.69114861272406*^9,
3.691148727494171*^9}, {3.691148763653823*^9, 3.691149183356879*^9},
3.691149220568158*^9, 3.691149288586091*^9, {3.691149376324484*^9,
3.691149382471024*^9}, 3.691149440231559*^9, {3.691149471944659*^9,
3.691149472938768*^9}, {3.691149519799526*^9, 3.691149996566272*^9}, {
3.691150029317634*^9, 3.691150032774948*^9}, {3.691150071692452*^9,
3.691150118533132*^9}, {3.691150179402705*^9, 3.69115043939212*^9}, {
3.6911505051660337`*^9, 3.691150532834193*^9}, {3.691158203206048*^9,
3.691158206342914*^9}, {3.6911583130270443`*^9, 3.691158313651495*^9},
3.691163908357132*^9, {3.6911640626639977`*^9, 3.691164108753628*^9}, {
3.691217685369544*^9, 3.69121776960758*^9}, {3.691217831026292*^9,
3.69121783428811*^9}, {3.691422782301071*^9, 3.691422808986714*^9}, {
3.691423215133719*^9, 3.6914232547830067`*^9}, 3.691423293510044*^9, {
3.691423352596332*^9, 3.691423469245451*^9}, {3.691423508997279*^9,
3.691423622554187*^9}, {3.691423662312357*^9, 3.691423805742711*^9}, {
3.691423906992992*^9, 3.691423916852833*^9}, {3.691423959847035*^9,
3.6914239872025347`*^9}, {3.691424076425527*^9, 3.691424104812086*^9}, {
3.691424139989594*^9, 3.691424150884856*^9}, {3.691424181996874*^9,
3.6914241945497093`*^9}, {3.6914242715328903`*^9, 3.691424271581215*^9}, {
3.691424303414624*^9, 3.691424338366431*^9}, {3.6914252003493357`*^9,
3.691425244768258*^9}, {3.6914252782644463`*^9, 3.6914254347805*^9}, {
3.691425471717619*^9, 3.691425473353613*^9}, 3.69142551683083*^9,
3.6914255829014397`*^9, 3.691425630619733*^9, {3.691425661720447*^9,
3.691425681821444*^9}, {3.691425741368102*^9, 3.691425771235519*^9}, {
3.6914258026173*^9, 3.691425935670659*^9}, {3.691425996353429*^9,
3.691426103561493*^9}, 3.6914261357732964`*^9, {3.6914262177974358`*^9,
3.6914264798706207`*^9}, {3.693639843555154*^9, 3.693639846797533*^9}, {
3.693656770818716*^9, 3.693656777778264*^9}, {3.69365697351645*^9,
3.693657018941032*^9}, {3.6936570687643957`*^9, 3.693657079477309*^9}, {
3.693657165459156*^9, 3.693657276863092*^9}, {3.69365730823442*^9,
3.6936573161015387`*^9}, {3.693657362099784*^9, 3.693657578572526*^9}, {
3.6936579660417137`*^9, 3.693657984505821*^9}, {3.6936599718857327`*^9,
3.693659983730382*^9}, {3.69366001436698*^9, 3.693660014878777*^9}, {
3.693660154126699*^9, 3.6936601554008627`*^9}, {3.699293848302413*^9,
3.699293897914488*^9}, {3.699293928710236*^9, 3.6992939726206512`*^9}, {
3.699294063235395*^9, 3.6992941501089973`*^9}, {3.699294229732108*^9,
3.6992942774972277`*^9}, {3.699294324115242*^9, 3.699294340974185*^9}, {
3.699294375965117*^9, 3.6992943908377857`*^9}, {3.699294426968742*^9,
3.699294448785288*^9}, {3.699294481737021*^9, 3.699294530049263*^9}, {
3.699294627942054*^9, 3.6992946452720947`*^9}, {3.699294849121073*^9,
3.6992948550678673`*^9}, {3.699294895168027*^9, 3.69929494196061*^9},
3.699294985927828*^9, {3.699295016239889*^9, 3.699295019235536*^9}, {
3.69929505281318*^9, 3.699295066315386*^9}, 3.699299459750135*^9, {
3.699340756079802*^9, 3.699340764631983*^9}, {3.699340824503377*^9,
3.699340933939489*^9}, {3.69934829774924*^9, 3.699348313303583*^9}, {
3.69934856418379*^9, 3.69934871208121*^9}, {3.709997243334426*^9,
3.7099973009674597`*^9}, {3.710821722798584*^9, 3.710821726478475*^9}, {
3.710821768718965*^9, 3.7108218062081823`*^9}, {3.710821839413843*^9,
3.710821871923889*^9}}],
Cell[BoxData[
GraphicsBox[{{}, {InsetBox[
GraphicsBox[{{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.], LineBox[CompressedData["
1:eJwBkQJu/SFib1JlAgAAACgAAAACAAAAgr9zjJmZyb8cZ8fgQ/rJvzKmF7iV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"]],
LineBox[CompressedData["
1:eJwBcQKO/SFib1JlAgAAACYAAAACAAAAnlMrVd/7XD94Na+H4RDQP5l+fcy2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"]]}, {}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox["\"z\"", TraditionalForm],
FormBox["\"P(z)\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
RGBColor[0, 0, 1], Bold, FontFamily -> "Helvetica"],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{-0.2, 0.1}, {-0.2029499862244898, 0.4726499861142857}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}], {192., -116.80842387373012`},
ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}], InsetBox[
GraphicsBox[{{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.], LineBox[CompressedData["
1:eJwV2Hc8lW8UAPBLVEplZQsNUUISEo5xXVeI7Fz1E2VlFZVVGWWFJERDJQnZ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"]]}}, {{}, {}, {}}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{
FormBox["\"z\"", TraditionalForm],
FormBox["\"F(z)\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->Directive[
RGBColor[0, 0, 1], Bold, FontFamily -> "Helvetica"],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{-0.01, 0.47}, {-0.0007656543551562145,
0.02268063531959396}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}], {576., -116.80842387373012`},
ImageScaled[{0.5, 0.5}], {360., 222.49223594996212`}]}, {}},
ContentSelectable->True,
PlotRangePadding->{6, 5}]], "Output",
CellChangeTimes->{{3.699340739683754*^9, 3.6993407654950943`*^9}, {
3.699340826663845*^9, 3.699340934443329*^9}, {3.6993482987669783`*^9,
3.699348313912451*^9}, {3.699348566073593*^9, 3.699348712609359*^9}, {
3.709997288519692*^9, 3.709997302148498*^9}, {3.710821697516238*^9,
3.710821727164421*^9}, 3.710821772569436*^9, 3.7108218066543627`*^9, {
3.7108218455623693`*^9, 3.710821872652583*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"detJ=\"\>", "\[InvisibleSpace]",
RowBox[{"-", "0.6000000000000014`"}]}],
SequenceForm["detJ=", -0.6000000000000014],
Editable->False]], "Print",
CellChangeTimes->{{3.69365720603776*^9, 3.693657279736801*^9},
3.693657440501865*^9, 3.6936575252977552`*^9, {3.693657563333323*^9,
3.6936575802798347`*^9}, 3.693659984444887*^9, 3.693660073250341*^9,
3.693660156208268*^9, {3.699293876947016*^9, 3.6992938988931637`*^9}, {
3.699293931386125*^9, 3.699293974871855*^9}, {3.6992940823986*^9,
3.699294150470052*^9}, {3.6992942321600647`*^9, 3.6992942781500273`*^9}, {
3.699294326814104*^9, 3.699294341712192*^9}, 3.699294395072814*^9, {
3.699294428932578*^9, 3.699294449734123*^9}, {3.6992944895188417`*^9,
3.699294530472254*^9}, {3.699294632018118*^9, 3.699294646125841*^9},
3.699294856200614*^9, 3.699294905784671*^9, 3.699294986377092*^9,
3.69929501989784*^9, 3.699295067126821*^9, 3.699340616755065*^9, {
3.699340738896171*^9, 3.699340765413507*^9}, {3.699340826583373*^9,
3.699340934362507*^9}, {3.6993482986898623`*^9, 3.6993483138324757`*^9}, {
3.6993485659944973`*^9, 3.699348712529565*^9}, {3.7099972885371323`*^9,
3.709997302163662*^9}, {3.7108216975316467`*^9, 3.710821727188814*^9},
3.710821772585013*^9, 3.710821806670178*^9, {3.710821845583539*^9,
3.7108218726678543`*^9}}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"The zero crossing of P is z0=\"\>", "\[InvisibleSpace]",
RowBox[{"-", "0.1098`"}]}],
SequenceForm["The zero crossing of P is z0=", -0.1098],
Editable->False]], "Print",
CellChangeTimes->{{3.69365720603776*^9, 3.693657279736801*^9},
3.693657440501865*^9, 3.6936575252977552`*^9, {3.693657563333323*^9,
3.6936575802798347`*^9}, 3.693659984444887*^9, 3.693660073250341*^9,
3.693660156208268*^9, {3.699293876947016*^9, 3.6992938988931637`*^9}, {
3.699293931386125*^9, 3.699293974871855*^9}, {3.6992940823986*^9,
3.699294150470052*^9}, {3.6992942321600647`*^9, 3.6992942781500273`*^9}, {
3.699294326814104*^9, 3.699294341712192*^9}, 3.699294395072814*^9, {
3.699294428932578*^9, 3.699294449734123*^9}, {3.6992944895188417`*^9,
3.699294530472254*^9}, {3.699294632018118*^9, 3.699294646125841*^9},
3.699294856200614*^9, 3.699294905784671*^9, 3.699294986377092*^9,
3.69929501989784*^9, 3.699295067126821*^9, 3.699340616755065*^9, {
3.699340738896171*^9, 3.699340765413507*^9}, {3.699340826583373*^9,
3.699340934362507*^9}, {3.6993482986898623`*^9, 3.6993483138324757`*^9}, {
3.6993485659944973`*^9, 3.699348712529565*^9}, {3.7099972885371323`*^9,
3.709997302163662*^9}, {3.7108216975316467`*^9, 3.710821727188814*^9},
3.710821772585013*^9, 3.710821806670178*^9, {3.710821845583539*^9,
3.710821872670569*^9}}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"Four zero crossings of F are z1=\"\>", "\[InvisibleSpace]",
"0.10862464785042454`", "\[InvisibleSpace]", "\<\", z2=\"\>",
"\[InvisibleSpace]", "0.1775132667072557`",
"\[InvisibleSpace]", "\<\", z3=\"\>", "\[InvisibleSpace]",
"0.3290164249781881`", "\[InvisibleSpace]", "\<\", z4=\"\>",
"\[InvisibleSpace]", "0.38860475062326694`"}],
SequenceForm[
"Four zero crossings of F are z1=", 0.10862464785042454`, ", z2=",
0.1775132667072557, ", z3=", 0.3290164249781881, ", z4=",
0.38860475062326694`],
Editable->False]], "Print",
CellChangeTimes->{{3.69365720603776*^9, 3.693657279736801*^9},
3.693657440501865*^9, 3.6936575252977552`*^9, {3.693657563333323*^9,
3.6936575802798347`*^9}, 3.693659984444887*^9, 3.693660073250341*^9,
3.693660156208268*^9, {3.699293876947016*^9, 3.6992938988931637`*^9}, {
3.699293931386125*^9, 3.699293974871855*^9}, {3.6992940823986*^9,
3.699294150470052*^9}, {3.6992942321600647`*^9, 3.6992942781500273`*^9}, {
3.699294326814104*^9, 3.699294341712192*^9}, 3.699294395072814*^9, {
3.699294428932578*^9, 3.699294449734123*^9}, {3.6992944895188417`*^9,
3.699294530472254*^9}, {3.699294632018118*^9, 3.699294646125841*^9},
3.699294856200614*^9, 3.699294905784671*^9, 3.699294986377092*^9,
3.69929501989784*^9, 3.699295067126821*^9, 3.699340616755065*^9, {
3.699340738896171*^9, 3.699340765413507*^9}, {3.699340826583373*^9,
3.699340934362507*^9}, {3.6993482986898623`*^9, 3.6993483138324757`*^9}, {
3.6993485659944973`*^9, 3.699348712529565*^9}, {3.7099972885371323`*^9,
3.709997302163662*^9}, {3.7108216975316467`*^9, 3.710821727188814*^9},
3.710821772585013*^9, 3.710821806670178*^9, {3.710821845583539*^9,
3.710821872674622*^9}}],
Cell[BoxData[
InterpretationBox[
RowBox[{"\<\"Four steady states of the SSN are re1=\"\>",
"\[InvisibleSpace]", "0.11925857467502134`",
"\[InvisibleSpace]", "\<\", ri1=\"\>", "\[InvisibleSpace]",
"0.0012816963412298388`", "\[InvisibleSpace]", "\<\"; re2=\"\>",
"\[InvisibleSpace]", "0.2743855351334897`",
"\[InvisibleSpace]", "\<\", ri2=\"\>", "\[InvisibleSpace]",
"0.0055936134213117`", "\[InvisibleSpace]", "\<\"; re3=\"\>",
"\[InvisibleSpace]", "1.0263488816675757`",
"\[InvisibleSpace]", "\<\", ri3=\"\>", "\[InvisibleSpace]",
"0.035616622834469376`", "\[InvisibleSpace]", "\<\"; re4=\"\>",
"\[InvisibleSpace]", "1.5472972037552453`",
"\[InvisibleSpace]", "\<\", ri4=\"\>", "\[InvisibleSpace]",
"0.05868462265659892`"}],
SequenceForm[
"Four steady states of the SSN are re1=", 0.11925857467502134`, ", ri1=",
0.0012816963412298388`, "; re2=", 0.2743855351334897, ", ri2=",
0.0055936134213117, "; re3=", 1.0263488816675757`, ", ri3=",
0.035616622834469376`, "; re4=", 1.5472972037552453`, ", ri4=",
0.05868462265659892],
Editable->False]], "Print",
CellChangeTimes->{{3.69365720603776*^9, 3.693657279736801*^9},
3.693657440501865*^9, 3.6936575252977552`*^9, {3.693657563333323*^9,
3.6936575802798347`*^9}, 3.693659984444887*^9, 3.693660073250341*^9,
3.693660156208268*^9, {3.699293876947016*^9, 3.6992938988931637`*^9}, {
3.699293931386125*^9, 3.699293974871855*^9}, {3.6992940823986*^9,
3.699294150470052*^9}, {3.6992942321600647`*^9, 3.6992942781500273`*^9}, {
3.699294326814104*^9, 3.699294341712192*^9}, 3.699294395072814*^9, {
3.699294428932578*^9, 3.699294449734123*^9}, {3.6992944895188417`*^9,
3.699294530472254*^9}, {3.699294632018118*^9, 3.699294646125841*^9},
3.699294856200614*^9, 3.699294905784671*^9, 3.699294986377092*^9,
3.69929501989784*^9, 3.699295067126821*^9, 3.699340616755065*^9, {
3.699340738896171*^9, 3.699340765413507*^9}, {3.699340826583373*^9,
3.699340934362507*^9}, {3.6993482986898623`*^9, 3.6993483138324757`*^9}, {
3.6993485659944973`*^9, 3.699348712529565*^9}, {3.7099972885371323`*^9,
3.709997302163662*^9}, {3.7108216975316467`*^9, 3.710821727188814*^9},
3.710821772585013*^9, 3.710821806670178*^9, {3.710821845583539*^9,
3.710821872678624*^9}}]
}, Open ]],
Cell[BoxData[
GraphicsBox[{{}, {
{GrayLevel[0],
{Arrowheads[{{0.04687896345853284, 1.}}], ArrowBox[CompressedData["
1:eJwBoQJe/SFib1JlAgAAACkAAAACAAAAMM4Z4qr30b/mSSnQd7+sP1VJbts0
i9G/iKjjK+4RrD+s7NHJZmPQv+CtHHakOKo/aE31b6qbzr+6CpFZiHyoP7W9
NifPssq/+Mor7NhbpT9Z+hFlf0rHv+JhDoT/oaI/HBr4sWJRxL8XSJPBG0Gg
P+5tMfoqqMC/5K/oKaummj+G/sHGnEu7v9H+ZwUX1pU/sTIXriBvur9a9Xi+
syWVP5qZmZmZmbm/exSuR+F6lD+Al4HGD9m2vwBGAdI/R5I/crASgj5ktL8o
jagBMlCQP9qQDHfoArC/W4F6vkCeiT9UVSyNnCepv0FE8HCwH4Q/WQXdBQPD
o79X1ZQ8a55/P3/JbFhRCpa/IhzgC26pcT+ojlyvsTKHvyzcN3r0N2Q/X5Lk
ov/Car/gN/6br31XPy9yfzd97WY/zxlmNb34TT9j1dTeIZiBP3SfdNnrzkI/
QROrMAg6jT8hHNLJ87E3P+PmSvv5LpA/tvIfj4H1ND+ewFf6ELuRP+SWa0wx
jjI/WTkJ4StDkz+3PL5atXowP+8MJ2LF1JQ/Q4WON7hFLT8Kxq7BRmGWP6sW
Z7SPJCo/L5DiNFjolz+7VgE5AIInPzBIy/Wbd5k/3zOf4lg9JT+ratkEeACb
P2xZCpymYyM/3Wsig7eCnD8IQJ8FnughP2S47eXkuJ0/PXO7jA3yID+xlnzV
K3ukP6E9Zf2QtBw/IdJNzPdEqT95tjycY20kP/j8UAKqTa0/dIkv8vH0LT8a
Ee7aHcayPxDjOgxp/zs/Gh00/peAtT908zF05mxDP6xfKjw3X7c/8tB2+/uc
Rz8IhsDxete4P0WN2iXVWUs/GqLhRNoKuj+paojIH6hOP/mLVo7dGLs/1N7d
ohK1UD8eQERz
"]]}},
{GrayLevel[0],
{Arrowheads[{{0.041065340528017955`, 1.}}], ArrowBox[CompressedData["
1:eJwBUQKu/SFib1JlAgAAACQAAAACAAAAGHMUqcOulL8RZrro5tqBv6kTADLW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"]]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwB0QEu/iFib1JlAgAAABwAAAACAAAALzTcrq7f8j8RZrro5tqBvyjCuzOe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"]]},
{Arrowheads[{{0.0013932551525751083`, 1.}}],
ArrowBox[{{1.7356747231934557`, 0.03072306592121211}, {
1.741803997209589, 0.031147884442963708`}, {1.7472972037552452`,
0.03152774944012187}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBkQFu/iFib1JlAgAAABgAAAACAAAAfvcP5xHP2D8RZrro5tqBv6wuXKTC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"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwB4QEe/iFib1JlAgAAAB0AAAACAAAA6srzcg827j9bqpSPPUWZPxY9AAX9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"]]},
{Arrowheads[{{0.05304411589913132, 1.}}], ArrowBox[CompressedData["
1:eJwBkQFu/iFib1JlAgAAABgAAAACAAAA2LkUuZ6T9z9erkFVf1qsP1nEcCOQ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"]]}},
{GrayLevel[0],
{Arrowheads[{{0.04133100022392696, 1.}}], ArrowBox[CompressedData["
1:eJwBwQE+/iFib1JlAgAAABsAAAACAAAAGzTOyeik+z9gVgzAUJWxPxFxzbyC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"]]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwB0QEu/iFib1JlAgAAABwAAAACAAAAEvcmkjI2+D9gVgzAUJWxPwAAAAAA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"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwB0QEu/iFib1JlAgAAABwAAAACAAAAJJioAsyb7j/t0bRtrmGkP0zxUxKf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"]]},
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBQQK+/SFib1JlAgAAACMAAAACAAAAm+BqFJaW2T8+aSzCDe+FP2x/I54A
iNk/25vMlVHWhT+m71Qya1fYP0Y1vbSqzYM/69BjSS601z+JzJJIPLGCP5nV
aRUiWtc/SDzSZWsOgj9XJOehujXXP6hA9qsyxYE/yo5ZtTAt1z+4NnpScaqB
P6JBCwUbPtc/pQ0MSB6ugT/niP+ROE/XP3gUO/0zvoE/nmSRSLtj1z86lTTx
ntOBP29X6pQwetc/aFo+VSDsgT8SOBDa6JHXP6E5qr6RBoI/agilzmaq1z+L
tMGNMiKCP+Y3tfdkSNg/dWFx6rzWgj9SHjRnsvfYPzwygKW3oYM/yQlwaTa3
2T9a1mSwP4GEP7JvjPrkRds/ZcR+UepYhj8GYpltfQ3dP+YaqwkKe4g/muT6
8I4I3z9OfmMEHOWKP8GOv4FgDOA/+3p4sEk1jD9pEEj1LJvgP9shhtSrl40/
lloCnu4t4T8QhepSMgaPPx2g+LmuwuE/SGsOXXo+kD9IBlmx9FriPydwcMeh
/5A/XbJR7Ef44j8fNv2qN8iRP8yjdZd29eM/rkY8MZgOkz8eQceKr/DkP0ed
2W0gV5Q/oo1LeiPm5T++e9ZOF5qVP8FtQjJi0eY//+nlzb3Rlj9ou24LPLHn
P4qCpqnJ+5c/RZLrggeC6D8wdnCaxxKZP3gf8o65bOk/K2uFRT9Omj9YOf3a
0z7qP3MILXlaaZs/8NHLFuH56j+K0+cBWGacPydYQ8aUF+s/oZoxMp+OnD+t
2RIF
"]]},
{Arrowheads[{{0.013563930377694539`, 1.}}],
ArrowBox[{{0.8814385825963816, 0.029365615378625563`}, {
0.8957606336781073, 0.02997755484948713}, {0.9222244404420676,
0.031115498623497845`}, {0.9504237569145363, 0.03233247569766802}, {
0.9706618972619726, 0.033216370313092554`}, {0.9859358927458397,
0.033846893353603705`}, {0.9904372069878413, 0.03413911175342361}, {
0.9861274844845557, 0.03389768613518458}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBwQE+/iFib1JlAgAAABsAAAACAAAAj4ESIPlf6j9gVgzAUJWxP8Qucsy9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"]]},
{Arrowheads[{{0.028860936174951033`, 1.}}],
ArrowBox[{{0.2686790133350163, 0.022389917777918027`}, {
0.26753753998876206`, 0.022294794999063505`}, {0.242410605182357,
0.020200883765196416`}, {0.21953971790452684`, 0.0182949764920439}, {
0.1987347162871762, 0.016561094384258783`}, {0.17992729568410876`,
0.014993338001839253`}, {0.1628968299217543, 0.013573208710601786`}, {
0.1474226928265427, 0.012282207876362859`}, {0.12076444810080444`,
0.010051535134312757`}, {0.09919464843340688, 0.008229206886553186}, {
0.08186150410534604, 0.006739472765765661}, {0.06807112283086962,
0.005521913972532075}, {0.04660386749783553, 0.003495422102306679}, {
0.035002577532831994`, 0.0022067274430240006`}, {0.02972722853352891,
0.001393411722842523}, {0.02837584986343774,
0.0008841633620723373}}]}},
{GrayLevel[0],
{Arrowheads[{{0.0625, 1.}}], ArrowBox[CompressedData["
1:eJwBoQFe/iFib1JlAgAAABkAAAACAAAA8AZ0aXNq6j8RZrro5tqBvzTVcf3T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"]]},
{Arrowheads[{{0.04381140769588504, 1.}}], ArrowBox[CompressedData["
1:eJwBUQGu/iFib1JlAgAAABQAAAACAAAAw1ePJnQb9j/qUpFlnVWdP025bd6C
XfY/XO2tv99pnj8GPIQOx7r2Pxt5KDH17p8/zGuH5YEV9z9rR38ATrSgPybO
EPrybfc/p0N4KwFsoT8UYyBMGsT3P0IxfxmUHqI/mCq22/cX+D87EJTKBsyi
Pz+O+DCvdfg/upgaXHaNoz9yzhPZFtH4P0YBgq7MSaQ/NOsH1C4q+T/iScrB
CQGlP4Dk1CH3gPk/iHLzlS2zpT9bunrCb9X5P0B7/So4YKY/w2z5tZgn+j8E
ZOiAKQinP7j7UPxxd/o/1Sy0lwGrpz84Z4GV+8T6P7XVYG/ASKg/n0uJ/40Q
+z/ClX/7MeKoP0VFZ7iBWvs/H6ShLyJ4qT8qVBvA1qL7P8oAxwuRCqo/THil
Fo3p+z/Cq++PfpmqPyBWqOnt9Ps/x2QjZXSwqj9cW6Fe
"]]}}}},
AspectRatio->1,
DisplayFunction->Identity,
Epilog->{
PointSize[0.04],
PointBox[{{0.11925857467502134`, 0.0012816963412298388`}, {
0.2743855351334897, 0.0055936134213117}, {1.0263488816675757`,
0.035616622834469376`}, {1.5472972037552453`, 0.05868462265659892}},
VertexColors -> {
GrayLevel[0],
RGBColor[0, 0, 1],
GrayLevel[0],
RGBColor[0, 0, 1]}]},
Frame->True,
FrameTicks->{{None, None}, {None, None}},
GridLines->{{{0.11925857467502134`,
GrayLevel[0]}, {0.2743855351334897,
RGBColor[0, 0, 1]}, {1.0263488816675757`,
GrayLevel[0]}, {1.5472972037552453`,
RGBColor[0, 0, 1]}}, {{0.0012816963412298388`,
GrayLevel[0]}, {0.0055936134213117,
RGBColor[0, 0, 1]}, {0.035616622834469376`,
GrayLevel[0]}, {0.05868462265659892,
RGBColor[0, 0, 1]}}},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
Method->{
"DefaultBoundaryStyle" -> Automatic, "TransparentPolygonMesh" -> True},
PlotRange->{{-0.2807414253249787,
1.7472972037552452`}, {-0.008718303658770162, 0.06868462265659891}},
PlotRangeClipping->True,
PlotRangePadding->{{0, 0}, {0, 0}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.699340739683754*^9, 3.6993407654950943`*^9}, {
3.699340826663845*^9, 3.699340934443329*^9}, {3.6993482987669783`*^9,
3.699348313912451*^9}, {3.699348566073593*^9, 3.699348712609359*^9}, {
3.709997288519692*^9, 3.709997302148498*^9}, {3.710821697516238*^9,
3.710821727164421*^9}, 3.710821772569436*^9, 3.7108218066543627`*^9, {
3.7108218455623693`*^9, 3.710821874105384*^9}}]
}, Open ]],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.709286937522565*^9, 3.709286956604727*^9},
3.709287029773843*^9}]
},
WindowSize->{971, 781},
WindowMargins->{{158, Automatic}, {Automatic, 0}},
PrintingCopies->1,
PrintingPageRange->{1, Automatic},
FrontEndVersion->"10.1 for Mac OS X x86 (32-bit, 64-bit Kernel) (March 23, \
2015)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 28949, 720, 1406, "Input"],
Cell[29531, 744, 9599, 171, 134, "Output"],
Cell[CellGroupData[{
Cell[39155, 919, 2472, 36, 21, "Print"],
Cell[41630, 957, 2557, 37, 22, "Print"],
Cell[44190, 996, 2573, 37, 22, "Print"],
Cell[46766, 1035, 2708, 41, 22, "Print"]
}, Open ]],
Cell[49489, 1079, 23793, 428, 375, "Output"]
}, Open ]],
Cell[73297, 1510, 92, 1, 28, "Input"],
Cell[CellGroupData[{
Cell[73414, 1515, 27647, 733, 1525, "Input"],
Cell[101064, 2250, 14178, 246, 134, "Output"],
Cell[CellGroupData[{
Cell[115267, 2500, 914, 16, 21, "Print"],
Cell[116184, 2518, 978, 16, 22, "Print"],
Cell[117165, 2536, 1100, 19, 22, "Print"],
Cell[118268, 2557, 1383, 24, 22, "Print"]
}, Open ]],
Cell[119666, 2584, 22332, 400, 375, "Output"]
}, Open ]],
Cell[142013, 2987, 92, 1, 28, "Input"],
Cell[CellGroupData[{
Cell[142130, 2992, 26424, 736, 1576, "Input"],
Cell[168557, 3730, 15418, 274, 134, "Output"],
Cell[CellGroupData[{
Cell[184000, 4008, 630, 12, 21, "Print"],
Cell[184633, 4022, 714, 13, 22, "Print"],
Cell[185350, 4037, 958, 18, 22, "Print"],
Cell[186311, 4057, 1355, 25, 40, "Print"]
}, Open ]],
Cell[187681, 4085, 28641, 519, 375, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[216359, 4609, 33462, 855, 1746, "Input"],
Cell[249824, 5466, 17233, 306, 134, "Output"],
Cell[CellGroupData[{
Cell[267082, 5776, 1395, 22, 21, "Print"],
Cell[268480, 5800, 1417, 22, 22, "Print"],
Cell[269900, 5824, 1797, 29, 22, "Print"],
Cell[271700, 5855, 2316, 38, 38, "Print"]
}, Open ]],
Cell[274031, 5896, 13054, 245, 409, "Output"]
}, Open ]],
Cell[287100, 6144, 118, 2, 28, "Input"]
}
]
*)
(* End of internal cache information *)