External and mutual synchronization of chimeras in a two layer network of nonlinear oscillators

TL;DR

This paper investigates how chimera states in two-layer networks of chaotic logistic maps synchronize externally and mutually, revealing conditions and regions where synchronization occurs, and relating findings to classical oscillation synchronization theory.

Contribution

It introduces a detailed numerical analysis of external and mutual synchronization of chimera states in coupled chaotic networks with different parameters.

Findings

Synchronization regions are identified using cross-correlation coefficients.

Unidirectional coupling leads to external synchronization in non-identical networks.

Symmetric coupling results in mutual synchronization with identical chimera structures.

Abstract

We study numerically synchronization phenomena of spatiotemporal structures, including chimera states, in a two layer network of nonlocally coupled nonlinear chaotic discrete-time systems. Each of the interacting ensembles represents a one layer ring network of nonlocally coupled logistic maps in the chaotic regime. The coupled networks differ in their control parameters that enables one to observe distinct spatiotemporal dynamics in the networks when there is no coupling between them. We explore in detail external and mutual synchronization of chimera structures. The identity of synchronous structures and the estimation of synchronization regions are quantified by calculating the cross-correlation coefficient between relevant oscillators of the networks. We show that for non-identical networks, unidirectional and symmetric couplings lead to external and mutual synchronization between the interacting ensembles, respectively. This is confirmed by identical synchronous structures and by the existence of finite regions of synchronization within which the cross-correlation coefficient is equal to 1. We also show that these findings are qualitatively equivalent to the results of the classical synchronization theory of periodic self-sustained oscillations.