If I have 2000 data points for the following equation ,How to find out the Lyapunov exponent for different values of [Tau] .This is a delay differential equation i.e infinite dimensional system.
b = 1;
V0 = 300;
I0 = 0.001;
N1 = 7/4;
p1 = (\[Pi]*b*N1)/V0;
a1 = 1.001; a2 = 0.123; a3 = -3.622*10^-3; b1 = 0.001959; b2 = 0.031;
b3 = 0.003241; G = 0.5*10^-5; \[CapitalOmega] = 0; C1 = p1/2000;
f = 1*10^3;
Is = 0.0;
\[Tau] = 15;
NL = 1000;
sol1[t_] =
NDSolve[{x'[t] - (I0*p1)/(
2*C1)*((a1*x[t - \[Tau]] - G/(p1*I0)*x[t]) -
3/4*x[t - \[Tau]]^3*a2 - 5/8*a3*x[t - \[Tau]]^5) -
Is*p1*Cos[y[t]] == 0,
y'[t] - \[CapitalOmega] - (I0*p1)/(
2*C1*x[t])*(b1*x[t - \[Tau]] + 3/4*x[t - \[Tau]]^3*b2 -
5/8*b3*x[t - \[Tau]]^5) + (Is*p1)/(2*C1*x[t])*Sin[y[t]] == 0,
x[0] == 0.003, y[0] == 0.001}, {x, y}, {t, 0, NL}]
