I post this question again with more details :
For a bachelor's work we have to study the chaotic behavior shown in the numerical solution of the driven van der pol oscillator as a function of the length of the Runge-Kutta step size. $$ y'' - \mu (1 - y^2)* y' + y = f(x) $$
My problem is that I can't find out for which parameter $\mu$ and function $f(x)$ this equation shows chaotic behavior, and what is the process to find these specific parameters?
By "chaotic behavior" I mean:
a small variation in the step length has a large variation in the topology of the solution.
I'll give you a little graphic of my current issue:
| graphical representation of the two numerical solutions with two different step lengths |
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The blue curve corresponds to a step size of $h=0.0089$. While for the orange one the step size is $h=0.0037$.
The equation that has been solved numerically corresponds to: $$ y'' - \mu (1 - y^2)* y' + y = A*sin(\omega*t) $$ with: $$\omega = \frac{2*\pi}{10},A=1.2, \mu = 8.53$$
and according to this page on Wikipedia (in the chapter "Forced Van der Pol oscillator") the solution should be chaotic, therefore sensitive to the step length. But as you can see the two solutions overlap and are not distinguishable. I can't find out why.
Thanks in advance for your answers!