Could Different Attractors Explain Variations in Lyapunov Exponents?

[Nono92]

Hi,

I am a beginner and I don't speak very well... So I'm really sorry for my poor scientific language...

I work on 1-Dimension time series of a same system measured at different periods. In these periods, time series have different chaotic characteristics as their lyapunov exponent are different.
To explain these lyapunov exponent differences, I hypothesize the system could have different number and/or type of attractor(s). Do you think that this hypothesis could be right ?

In order to verify this hypothesis, I've tried to observe these attractors.
I don't know if it exists methods to observe it. Do you know methods to observe it ?

As I am a beginner I have tried several methods may be not adaptated.
These are the methods that I have applied :
So, I have plotted poincare plot, I have observed that at several moment there are rotations around a center.
I have calculated for each three followed points a gravity center, I have evaluated hom many cluster could be identified with a gaussian model mixture method with Calinsky Harabasz algorithm. And then I have applied gaussian model mixture with the number of clusters calculated previously on these gravity centers.

But I don't know if it is really attractors that I observe with these methods.
Could you help me ?
Thanks a lot

nono92

 

[atyy]

Have you tried Ruelle-Takens embedding? http://www.scholarpedia.org/article/Attractor_reconstruction