Symmetry-breaking mechanism for the formation of cluster chimera patterns

TL;DR

This paper introduces a novel stability-breaking mechanism that explains the formation of cluster chimera patterns, where synchronized and incoherent groups coexist in coupled oscillator systems.

Contribution

It proposes a new approach to understand the emergence, stability, and robustness of chimera states through a stability-breaking method for synchronized clusters.

Findings

Clusters of synchronized oscillators can emerge via the proposed mechanism.

Cluster chimera states involve coexistence of coherent and incoherent groups.

The method provides insights into the stability of chimera patterns.

Abstract

The emergence of order in collective dynamics is a fascinating phenomenon that characterizes many natural systems consisting of coupled entities. Synchronization is such an example where individuals, usually represented by either linear or nonlinear oscillators, can spontaneously act coherently with each other when the interactions' configuration fulfills certain conditions. However, synchronization is not always perfect, and the coexistence of coherent and incoherent oscillators, broadly known in the literature as chimera states, is also possible. Although several attempts have been made to explain how chimera states are created, their emergence, stability, and robustness remain a long-debated question. We propose an approach that aims to establish a robust mechanism through which chimeras originate. We first introduce a stability-breaking method where clusters of synchronized oscillators can emerge. Similarly, one or more clusters of oscillators may remain incoherent within yielding a particular class of patterns that we here name cluster chimera states.