How Does Bifurcation in Dynamical Systems Influence Information Generation?

[Gargamel]

I would like to ask for a piece of advice on references on following issue:
Any (macroscopic) bifurcation of dynamical system generates some new information (or loss of information). In particular, when the dynamical system is loosing stability (i.e. stable equilibria becomes unstable) some new amount of information is obtained.
Still, I could not find any reference where this relation bifurcation-information is systematically explained. For instance, there are many different classifications of bifurcations, but I could not find any classification regarding the informational properties.
So, can anyone help with some references or some brief explanation on this?

 

[azntoon]

A good starting point for understanding the relation between bifurcations and information is the book "Bifurcation Theory and Applications" by Jean-Pierre Francoise (Springer, 2017). In this book, Francoise explains the concept of information in the context of dynamical systems and how bifurcations can be used to generate and measure it. He also discusses the various types of bifurcations that exist, how they can be classified, and how they affect the information content of a system. Additionally, Francoise provides a detailed overview of the mathematical tools used to analyze and study bifurcations and their implications for information theory.