Chaos synchronization with coexisting global fields

TL;DR

This paper explores chaos synchronization in coupled map systems influenced by both autonomous and external global fields, identifying conditions for complete and generalized synchronization states.

Contribution

It introduces a simple coupled map model demonstrating coexistence of two chaos synchronization states and analyzes their stability with minimal system size.

Findings

Complete synchronization to external field is achievable.

Generalized synchronization occurs even with identical drive and local maps.

Stable states are characterized across parameter space.

Abstract

We investigate the phenomenon of chaos synchronization in systems subject to coexisting autonomous and external global fields by employing a simple model of coupled maps. Two states of chaos synchronization are found: (i) complete synchronization, where the maps synchronize among themselves and to the external field, and (ii) generalized or internal synchronization, where the maps synchronize among themselves but not to the external global field. We show that the stability conditions for both states can be achieved for a system of minimum size of two maps. We consider local maps possessing robust chaos and characterize the synchronization states on the space of parameters of the system. The state of generalized synchronization of chaos arises even the drive and the local maps have the same functional form. This behavior is similar to the process of spontaneous ordering against an external field found in nonequilibrium systems.