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.

 

[Entropia]

I would first like to clarify that bifurcation refers to a point in a dynamical system where a small change in a parameter can cause a significant change in the behavior of the system. This can result in the creation of new stable states or the loss of stability in existing states.

In terms of information, it is important to understand that the concept of information can be applied in different ways in different disciplines. In the context of dynamical systems, information can refer to the amount of uncertainty or randomness in the system. The more unpredictable a system is, the more information it contains.

In regards to the relationship between bifurcation and information, there have been studies that have explored this topic. For example, in the field of information theory, researchers have looked at how bifurcations in dynamical systems can affect the amount of information that can be transmitted through the system. This is because bifurcations can create new pathways or limit the flow of information within the system.

Additionally, there have been studies that have examined the relationship between bifurcations and information in the context of complex systems and chaos theory. These studies have shown that as a system approaches a bifurcation point, there is an increase in the complexity and unpredictability of the system, which can be seen as an increase in the amount of information contained within the system.

In terms of references, I would recommend looking into papers and books by researchers such as James Gleick, Edward Lorenz, and Stuart Kauffman, who have studied the connection between bifurcation and information in the context of complex systems and chaos theory.

In summary, the relationship between bifurcation and information is a complex and multi-disciplinary topic. While there may not be a specific classification for bifurcations based on their informational properties, there is a growing body of research that explores this relationship and its implications in various fields. I hope this helps provide some insight and guidance for your research.