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Symmetries of Chimera States
Felix P Kemeth1,2, Sindre W Haugland1,2, Katharina Krischer1
1Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Strasse 1, D-85748 Garching, Germany.
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 setwise 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.
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