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-   -   Lyapunov in duffing and van der pol (http://mymathforum.com/math-software/23712-lyapunov-duffing-van-der-pol.html)

 dantekavala January 12th, 2012 03:27 AM

Lyapunov in duffing and van der pol

I have to make a program to calculate the largest lyapunov exponent for lorenz, rossler, duffing and van der pol. I did for the first two but i can't do it for the rest of them

The code i use for lorenz is this one:
Code:

```F[{x_, y_, z_}] := {? (y - x), x (r - z) - y, x y - b z}; JacobianMatrix[funs_List, vars_List] := Outer[D, funs, vars]; J =  JacobianMatrix[   F[{Subscript[y, 1][t], Subscript[y, 2][t],     Subscript[y, 3][t]}], {Subscript[y, 1][t], Subscript[y, 2][t],   Subscript[y, 3][t]}]; Y =  Table[{Subscript[y, i][t], Subscript[y, i + 3][t],   Subscript[y, i + 6][t]}, {i, 4, 6}]; E1 =  Flatten[Transpose[J.Y]]; EQ3 =  Table[D[Subscript[y, i][t], {t, 1}] ==   F[{Subscript[y, 1][t], Subscript[y, 2][t], Subscript[y, 3][t]}][[     i]], {i, 1, 3}]; EQ9 =  Table[D[Subscript[y, i][t], {t, 1}] == E1[[i - 3]], {i, 4,   12}]; YI9 =  Table[{Subscript[y, i][0] == If[Mod[i, 4] == 0, 1, 0],   Subscript[y, i + 3][0] == If[Mod[i + 3, 4] == 0, 1, 0],   Subscript[y, i + 6][0] == If[Mod[i + 6, 4] == 0, 1, 0]}, {i, 4, 6}]; YI3 = {Subscript[y, 1][0] == 19, Subscript[y, 2][0] == 20,   Subscript[y, 3][0] == 50}; sol1 =  NDSolve[Join[EQ9, EQ3, YI3, YI9],   Table[Subscript[y, i][t], {i, 1, 12}], {t, 0, 30},   MaxSteps -> Infinity]; u = Table[Random[], {3}]; T = 30; PhiT = Transpose[   Table[{Subscript[y, i][t], Subscript[y, i + 3][t],       Subscript[y, i + 6][t]}, {i, 4, 6}] /. sol1 /. t -> 30]; mle = Log[Norm[PhiT.u]]/T;```
Lorenz and rossler have 3 equation so i don't have problem. Duffing and van der pol have only one equation and i don't know what to do. I try a lot of things with this code but anyone has results

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