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 January 12th, 2012, 03:27 AM #1 Newbie   Joined: Jun 2011 Posts: 6 Thanks: 0 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

 Tags der, duffing, lyapunov, pol, van

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