Activated Mathematica Example 3

Activated Mathematica Example 3:

Taken from "4. Shaded Nullclines and Single ODEs"

In[32]:=

equation = x'[t] == If[Abs[x[t]] <= 2.5, x[t]^2 + t^2 - 1];
  Off[NDSolve::ndnum];
  
  shadedBackground = ContourPlot[
    equation[[2, 2]] /. x[t] -> x, {t, -2.5, 2.5}, {x, -2.5, 2.5},
      Contours -> 15, ContourLines -> False, PlotPoints -> 40,
      ColorFunction -> (GrayLevel[# 0.6 + 0.4]&),
      DisplayFunction -> Identity];
  
  thickNullcline = ContourPlot[
    equation[[2, 2]] /. x[t] -> x, {t, -2.5, 2.5}, {x, -2.5, 2.5},
      Contours -> {0}, ContourShading -> False, PlotPoints -> 40,
      ContourStyle -> {Thickness[0.015]},
      DisplayFunction -> Identity];
  
  initialVals = Table[1.5 {Cos[t], Sin[t]}, {t, 0, 2 Pi, N[Pi]/10}];
  
  solutions = x[t] /. Map[First[
    NDSolve[{equation, x[#[[1]]] == #[[2]]}, x[t], {t, -2.5, 2.5}]]&,
    initialVals];
  
  solutionImages = Table[
    Plot[Evaluate[solutions[[i]]], 
      {t, solutions[[i, 0, 1, 1]], solutions[[i, 0, 1, 2]]},
      PlotStyle -> {{AbsoluteThickness[2], Hue[1 - 0.8 i/21]}},
      DisplayFunction -> Identity],  {i, 21}];
  
  Show[{shadedBackground, thickNullcline, solutionImages}, 
  Graphics[{PointSize[0.02], Map[Point, initialVals]}],
  DisplayFunction -> $DisplayFunction, AspectRatio -> Automatic];

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