@Wrzlprmft, I rewrote my question after thinking about it in some more accessible ways to me, although it is rigorous like computing Lyapunov exponents. What do you think now? My idea is to perturb the state variable when it has settled to some final value and then see how it reacts, e.g will it return to that final value. My code currently doesn't do what I want it to do, though ...

not rigorous like Lyapunov

What do you think? Thanks @Wrzlprmft