Global interactions, information flow, and chaos synchronization

TL;DR

This paper explores how chaos synchronization in dynamical systems relates to information flow, showing that synchronization can occur with both homogeneous and heterogeneous global interactions, and that information measures can predict synchronization.

Contribution

It demonstrates that complete synchronization does not require homogeneous global fields and introduces information transfer as a predictor of synchronization in complex systems.

Findings

Synchronization can occur without homogeneous global fields.

Information transfer measures characterize and predict synchronization.

Maximum information transfer correlates with the onset of synchronization.

Abstract

We investigate the relationship between the emergence of chaos synchronization and the information flow in dynamical systems possessing homogeneous or heterogeneous global interactions whose origin can be external (driven systems) or internal (autonomous systems). By employing general models of coupled chaotic maps for such systems, we show that the presence of a homogeneous global field, either external or internal, for all times is not indispensable for achieving complete or generalized synchronization in a system of chaotic elements. Complete synchronization can also appear with heterogeneous global fields; it does not requires the simultaneous sharing of the field by all the elements in a system. We use the normalized mutual information and the information transfer between global and local variables to characterize complete and generalized synchronization. We show that these information measures can characterize both types of synchronized states and also allow to discern the origin of a global interaction field. A synchronization state emerges when a sufficient amount of information provided by a field is shared by all the elements in the system, on the average over long times. Thus, the maximum value of the top-down information transfer can be used as a predictor of synchronization in a system, as a parameter is varied.