Weak chimeras in minimal networks of coupled phase oscillators

Abstract

We suggest a definition for a type of chimera state that appears in networks of indistinguishable phase oscillators. Defining a "weak chimera" as a type of invariant set showing partial frequency synchronization, we show that this means they cannot appear in phase oscillator networks that are either globally coupled or too small. We exhibit various networks of four, six and ten indistinguishable oscillators where weak chimeras exist with various dynamics and stabilities. We examine the role of Kuramoto-Sakaguchi coupling in giving degenerate (neutrally stable) families of weak chimera states in these example networks.

9 figures

References in corpus (2)

• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Heteroclinic Ratchets in a System of Four Coupled Oscillators

Cited by in corpus (10)

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• Solitary states in the mean-field limit
• Mobility-induced persistent chimera states
• Chimera states for directed networks
• Chimera states in nonlocally coupled phase oscillators with biharmonic interaction