Repulsively Coupled Kuramoto-Sakaguchi Phase Oscillators Ensemble Subject to Common Noise

Abstract

We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state and leads to a nontrivial distribution of oscillator phases. In previous numerical simulations, a formation of stable multicluster states has been observed in this regime. However we argue here, that because identical phase oscillators in the Kuramoto-Sakaguchi model form a partially integrable system according to the Watanabe-Strogatz theory, the formation of clusters is impossible. Integrating with various time steps reveals that clustering is a numerical artifact, explained by the existence of higher order Fourier terms in the errors of the employed numerical integration schemes. Monitoring the induced change in certain integrals of motion we quantify these errors. We support these observations by showing, on the basis of the analysis of the corresponding Fokker-Planck equation, that two-cluster states are non-attractive. On the other hand, in ensembles of general limit cycle oscillators, such as Van der Pol oscillators, due to an anharmonic phase response function, as well as additional amplitude dynamics, multiclusters can occur naturally.

arXiv comment10 pages, 14 figures

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Cited by in corpus (7)

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• Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
• Exact finite-dimensional reduction for a population of noisy oscillators and its link to Ott-Antonsen and Watanabe-Strogatz theories
• Coupled Moebius Maps as a Tool to Model Kuramoto Phase Synchronization
• Optimal control for phase locking of synchronized oscillator populations via dynamical reduction techniques
• Diversity of dynamical behaviors due to initial conditions: exact results with extended Ott--Antonsen ansatz for identical Kuramoto--Sakaguchi phase oscillators
• A Coupled Oscillator Model for the Origin of Bimodality and Multimodality