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arXiv · 1404.7292

The Kuramoto model of coupled oscillators with a bi-harmonic coupling function

M. Komarov·A. Pikovsky
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Abstract

We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent equations describing uniformly rotating complex order parameters, both for single-branch (one possible state of locked oscillators) and multi-branch (two possible values of locked phases) entrainment. We show that synchronous states coexist with the neutrally linearly stable asynchronous regime. The latter has a finite life time for finite ensembles, this time grows with the ensemble size as a power law.

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M. Komarov, A. Pikovsky. 2014-04-29. The Kuramoto model of coupled oscillators with a bi-harmonic coupling function. https://doi.org/10.1016/j.physd.2014.09.002

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