Symmetry-broken states on networks of coupled oscillators

Abstract

When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here we show that alternative persistent states may also exist that break the symmetries of the underlying coupling network. We further show that these symmetry-broken coexistent states are analogous to those dubbed "chimera states," which can occur when identical oscillators are coupled to one another in identical ways.

arXiv comment6 pages, 6 figures

References in corpus (16)

• The structure and function of complex networks
• Synchronization in complex networks
• Chimera States for Coupled Oscillators
• The Kuramoto model in complex networks
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Spontaneous synchrony in power-grid networks
• Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
• The onset of synchronization in large networks of coupled oscillators
• Remote synchronization reveals network symmetries and functional modules
• Comparative analysis of existing models for power-grid synchronization
• Chimera States in a Ring of Nonlocally Coupled Oscillators
• Chimera states in heterogeneous networks
• Chimera states in networks of nonlocally coupled Hindmarsh-Rose neuron models
• Impact of network topology on synchrony of oscillatory power grids
• Topological Speed Limits to Network Synchronization
• Coexisting chaotic and multi-periodic dynamics in a model of cardiac alternans

Cited by in corpus (5)

• Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions
• Functional control of network dynamics using designed Laplacian spectra
• Chimera-like States in Structured Heterogeneous Networks
• Quasi-symmetries in complex networks: a dynamical model approach
• Chimera dynamics in nonlocally coupled moving phase oscillators