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

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.

References in corpus (2)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Impact of the electrical connection of N Spin Transfer Oscillators on their synchronization : an analytical study

Cited by in corpus (4)

• Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling
• Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings
• Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling
• Noise-induced stabilization of collective dynamics