Generalized synchronization of chaos in autonomous systems

TL;DR

This paper extends the concept of generalized synchronization of chaos from driven systems to autonomous spatiotemporal systems, revealing minimal conditions for their synchronized states and highlighting their similarities.

Contribution

It introduces a novel framework linking driven and autonomous systems, showing that similar stability conditions govern their generalized synchronization phenomena.

Findings

Synchronization can occur without the coupling depending on all variables.

Conditions for stability are equivalent in driven and autonomous systems.

Generalized synchronization is achievable under minimal interaction conditions.

Abstract

We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an autonomous system can be synchronized to each other but not to a coupling function defined from them. The form of the coupling function is not crucial; it may not depend on all the state variables nor it needs to be active for all times for achieving generalized synchronization. The procedure is based on the analogy between a response map subject to an external drive acting with a probability p and an autonomous system of coupled maps where a global interaction between the maps takes place with this same probability. It is shown that, under some circumstances, the conditions for stability of generalized synchronized states are equivalent in both types of systems. Our results reveal the existence of similar minimal conditions for the emergence of generalized synchronization of chaos in driven and in autonomous spatiotemporal systems.