I am trying to adapt the existing code from "Mathematica package for analysis and control of chaos in nonlinear system" by Gutierrez. This existing code calculates the Lyapunov Exponent by mapping method. I think it should work for more than 1D. It works for Logistic function (1D) but not for Henon function (2D).


 LyapunovExp[map_, x0_, n_] := 
 Plus @@ (Function[x, Evaluate[Log[Abs[D[map[x], x]]]]] /@ 
 Drop[Orbit[map, x0, n + 500], 500])/n

 Logistic[r_] := Function[x, r x (1 – x)];

 Plot[lya = LyapunovExp[Logistic[r], 0.5, 500], {r, 0, 4}, 
 PlotStyle -> Red]

 Henon[r_] := Function[x, {1 - r x[[1]]^2 + x[[2]], 1/3 x[[1]]}]

 Plot[LyapunovExp[Henon[r], {0.5, 0.5}, 150], {r, 0, 1.3}, 
 PlotStyle -> Red]

My guess is that the problem starts with function D which is not a proper way to evaluate derivative of the multivariable function. Am I right?


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