Stable Chimeras and Independently Synchronizable Clusters

TL;DR

This paper introduces a theoretical framework for analyzing cluster synchronization in networks, enabling the identification of stable chimera states by decoupling the stability of symmetry clusters.

Contribution

It establishes a method to divide symmetry clusters into independently synchronizable sets, facilitating the discovery of stable chimera states in symmetric networks.

Findings

Decoupling of cluster stability enhances understanding of synchronization patterns.

Framework enables identification of stable chimera states with mixed stability clusters.

Provides a new approach to analyze complex synchronization phenomena.

Abstract

Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we establish a theoretical basis to divide an arbitrary pattern of symmetry clusters into independently synchronizable cluster sets, in which the synchronization stability of the individual clusters in each set is decoupled from that in all the other sets. Using this framework, we suggest a new approach to find permanently stable chimera states by capturing two or more symmetry clusters---at least one stable and one unstable---that compose the entire fully symmetric network.