Symmetries of Chimera States

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.

References in corpus (12)

• Chimera States for Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
• Chimera states: The Existence Criteria Revisited
• Weak chimeras in minimal networks of coupled phase oscillators
• A classification scheme for chimera states
• Experimental observation of chimera and cluster states in a minimal globally coupled network
• Chimera states in networks of phase oscillators: the case of two small populations
• Chimeras in globally coupled oscillatory systems: From ensembles of oscillators to spatially continuous media
• Pattern formation during the oscillatory photoelectrodissolution of n-type silicon: Turbulence, clusters and chimeras
• Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions
• Isotropy of Angular Frequencies and Weak Chimeras With Broken Symmetry

Cited by in corpus (17)

• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Phase reduction beyond the first order: the case of the mean-field complex Ginzburg-Landau equation
• The changing notion of chimera states, a critical review
• Networks of coupled oscillators: from phase to amplitude chimeras
• Experimental investigation on the susceptibility of minimal networks to a change in topology and number of oscillators
• Cluster singularity: the unfolding of clustering behavior in globally coupled Stuart-Landau oscillators
• Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators
• Robust universal approach to identify travelling chimeras and synchronized clusters in spiking networks
• Attracting Poisson Chimeras in Two-population Networks
• Self-organized Multi-Frequency Clusters in an Oscillating Electrochemical System with Strong Nonlinear Coupling
• Dynamical Systems on Graph Limits and Their Symmetries
• A new class of chimeras in locally coupled oscillators with small-amplitude, high-frequency asynchrony and large-amplitude, low-frequency synchrony
• Chaotic Chimera Attractors in a Triangular Network of Identical Oscillators
• Variety of rotation modes in a small chain of coupled pendulums
• Connecting minimal chimeras and fully asymmetric chaotic attractors through equivariant pitchfork bifurcations
• Phase chimera states: frozen patterns of disorder
• Between Synchrony and Turbulence: Intricate Hierarchies of Coexistence Patterns