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Published on: May 30, 2014
Weak chimeras in minimal networks of coupled phase oscillators
Peter Ashwin1, Oleksandr Burylko2
1Centre for Systems, Dynamics and Control, Harrison Building, University of Exeter, Exeter EX4 4QF, United Kingdom.
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.
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