Symmetries of Chimera States
Chaotic Dynamics
2018-05-30 v2
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.
Keywords
Cite
@article{arxiv.1803.04542,
title = {Symmetries of Chimera States},
author = {Felix P. Kemeth and Sindre W. Haugland and Katharina Krischer},
journal= {arXiv preprint arXiv:1803.04542},
year = {2018}
}