Numerical studies on the synchronization of a network of mutually coupled simple chaotic systems

TL;DR

This paper investigates the synchronization phenomena in a network of coupled simple chaotic systems, revealing the existence of strange non-chaotic attractors and analyzing their stability through spectral and stability function methods.

Contribution

It introduces the study of strange non-chaotic attractors in a network of coupled systems and analyzes their synchronization behavior and stability.

Findings

Existence of strange non-chaotic attractors at low coupling strengths

Identification of synchronized and unsynchronized states in the network

Confirmation of stability of synchronization via Master Stability Function

Abstract

We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of synchronization behavior. The chaotic attractors of the simple $2 \times 2$ matrix network exhibiting strange non-chaotic attractors in their synchronization dynamics for smaller values of the coupling strength is reported. Further, the existence of islands of unsynchronized and synchronized states of strange non-chaotic attractors for smaller values of coupling strength is observed. The process of complete synchronization observed in the network with all the systems exhibiting strange non-chaotic behavior is reported. The variation of the slope of the singular continuous spectra as a function of the coupling strength confirming the strange non-chaotic state of each of the system in the network is presented. The stability of complete synchronization observed in the network is studied using the Master Stability Function.