Desynchronization transitions in nonlinearly coupled phase oscillators

Abstract

We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous state to partial synchrony is performed. We demonstrate that for small ensembles it is typically mediated by stable cluster states, that disappear with creation of heteroclinic cycles, while for a larger number of oscillators a direct transition from full synchrony to a periodic or quasiperiodic regime occurs.

25 pages, 8 figures

References in corpus (3)

• Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling
• Generalized coupling in the Kuramoto model
• Phase diagram of a generalized Winfree model

Cited by in corpus (9)

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• Chaos in generically coupled phase oscillator networks with nonpairwise interactions
• Hopf normal form with $S_N$ symmetry and reduction to systems of nonlinearly coupled phase oscillators
• Multi-clusters in networks of adaptively coupled phase oscillators networks
• Hierarchical frequency clusters in adaptive networks of phase oscillators
• Heteroclinic switching between chimeras
• Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling
• Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators
• Chaos in Coupled Heteroclinic Cycles and its Piecewise-Constant Representation