Gene

Physics

Statistical physics

Mathematical analysis

Artificial intelligence

Attractor

Chemistry

Invariant (physics)

Geometry

Chaotic

Symmetry (geometry)

Chimera (genetics)

Theoretical physics

Mathematics

Computer science

Biochemistry

Quantum mechanics

Homogeneous space

Physical Review Letters

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.

Symmetries of Chimera States