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Turing Stripes

By: Matthen on May 17th, 2013  |  syntax: None  |  size: 1.39 KB  |  views: 159  |  expires: Never
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  1. window[x_] := (Cos[Pi x] + 1)/2;
  2. n = 3;
  3. ps = {0.6, -0.3, 0.1};
  4. as = {0.1, 0.5, 0.8};
  5. initu[x_] := Sum[2 as[[i]] Exp[-20 (x - ps[[i]])^2], {i, n}];
  6. Tmax = 80;
  7. \[Tau] = 0.1; du2 = 0.00028; dv2 = 0.005; \[Kappa] = -0.005;
  8. soln = NDSolve[{
  9.     D[u[x, t], t] ==
  10.      du2  D[u[x, t], {x, 2}] + u[x, t] - u[x, t]^3 -
  11.       v[x, t] - \[Kappa],
  12.     \[Tau] D[v[x, t], t] ==
  13.      dv2  D[v[x, t], {x, 2}] + u[x, t] - v[x, t],
  14.     u[x, 0] == 0.5 window[x] x,
  15.     v[x, 0] == 0.1 window[x],
  16.     Derivative[1, 0][u][-1, t] == 0,
  17.     Derivative[1, 0][u][1, t] == 0,
  18.     Derivative[1, 0][v][-1, t] == 0,
  19.     Derivative[1, 0][v][1, t] == 0
  20.     }, {u, v}, {x, -1, 1}, {t, 0, Tmax}];
  21. frame[tt_] := Show[
  22.    ArrayPlot[{
  23.      Table[
  24.       Tanh[
  25.        3 Max[0, (First[(u[x, t] - v[x, t]) /. soln] /. {x -> xx,
  26.             t -> tt})]]^2,
  27.       {xx, -1, 1, 2/100}]}
  28.     , AspectRatio -> 1, ColorFunction -> "DeepSeaColors",
  29.     Frame -> False]
  30.    ,
  31.    Plot[
  32.     Max[0, (1 + First[(u[x, t] /. soln)] /. {x -> (xx - 50)/50,
  33.          t -> tt})/2]
  34.     , {xx, 0, 101}, PlotRange -> {-1, 1},
  35.     PlotStyle -> Directive[Thick, Red], Axes -> None],
  36.    Plot[
  37.     Max[0, (1 + First[(v[x, t] /. soln)] /. {x -> (xx - 50)/50,
  38.          t -> tt})/2]
  39.     , {xx, 0, 101}, PlotRange -> {-1, 1},
  40.     PlotStyle -> Directive[Thick, Yellow]],
  41.    ImageSize -> 300];
  42. Manipulate[
  43.  frame[Exp[tt] - 0.99],
  44.  {tt, 0, 3.5}
  45.  ]
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