Synchronization in networks of coupled hyperchaotic CO$_2$ lasers

TL;DR

This paper investigates synchronization phenomena in networks of hyperchaotic CO$_2$ lasers, demonstrating stable synchronization in specific network configurations and coupling conditions, with numerical validation and observation of chimera states.

Contribution

It introduces a non-autonomous dynamical system model and applies the master stability function to analyze synchronization in coupled hyperchaotic laser networks, including numerical simulations.

Findings

Stable synchronization achieved in networks of up to 24 lasers.

Synchronization error less than 10^{-6} in simulations.

Chimera states coexist with synchronized states under certain conditions.

Abstract

A non-autonomous dynamical system is proposed to study the synchronization in networks of mutually coupled optically modulated hyperchaotic CO$_2$ lasers. By the method of master stability function (MSF) it is shown that the stable synchronous state can be reached for both the ring of diffusively coupled (RDC) and star-coupled (SC) networks of at most $24$ nodes or oscillators. A numerical simulation of the coupled $24$ hyperchaotic CO$_2$ lasers is also performed to show that the corresponding synchronization error $\lesssim10^{-6}$. Furthermore, the chimera states of the networks are found to coexist in some intervals of time and the coupling strengths where the networks are not synchronized, implying that the synchronization occurs only in some specific ranges of values of the coupling strengths.