Synchronized states in chaotic systems coupled indirectly through a dynamic environment

TL;DR

This paper investigates various synchronization phenomena in chaotic systems coupled indirectly via a dynamic environment, analyzing stability and transitions through numerical and analytical methods.

Contribution

It introduces a comprehensive analysis of synchronization types in chaotic systems coupled through a dynamic environment, including stability conditions and transition mechanisms.

Findings

Multiple synchronization states observed, including in-phase, anti-phase, complete, and anti-synchronization.

Numerical results align with stability analysis predictions.

Transitions between synchronization states depend on coupling parameters.

Abstract

We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization behavior, such as in-phase, anti-phase,complete and anti- synchronization is possible. We present an approximate stability analysis for the different synchronization behaviors. The transitions to different states of synchronous behaviour are analyzed in the parameter plane of coupling strengths by numerical studies for specific cases such as Rossler and Lorenz systems and are characterized using various indices such as correlation, average phase difference and Lyapunov exponents. The threshold condition obtained from numerical analysis is found to agree with that from the stability analysis.