title: 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.
authors: Centre for Systems, Dynamics and Control, Harrison Building, University of Exeter, Exeter EX4 4QF, United Kingdom.
authors: Peter
authors: P
authors: Ashwin
authors: Institute of Mathematics, National Academy of Sciences, 01601 Kyiv, Ukraine.
authors: Oleksandr
authors: O
authors: Burylko