Symmetries of Chimera States

TL;DR

This paper analyzes the symmetry properties of chimera states in small networks of coupled oscillators, classifying different types based on their invariance under permutation symmetries, and discusses their relation to spatially extended systems.

Contribution

It introduces a classification scheme for chimera states based on their symmetry properties in small oscillator networks, linking them to larger spatial systems.

Findings

Chimera states exhibit different set-wise symmetries in incoherent oscillators.

Some chimera states are invariant under permutation symmetry, others are not.

The symmetry properties of small network chimera states relate to those in extended spatial systems.

Abstract

Symmetry broken states arise naturally in oscillatory networks. In this Letter, we investigate chaotic attractors in an ensemble of four mean-coupled Stuart-Landau oscillators with two oscillators being synchronized. We report that these states with partially broken symmetry, so-called chimera states, have different set-wise symmetries in the incoherent oscillators, and in particular some are and some are not invariant under a permutation symmetry on average. This allows for a classification of different chimera states in small networks. We conclude our report with a discussion of related states in spatially extended systems, which seem to inherit the symmetry properties of their counterparts in small networks.