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

  • 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. (C) 2014 Elsevier B.V. All rights reserved.

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Metadaten
Author:Maxim Komarov, Arkady S. PikovskyORCiDGND
DOI:https://doi.org/10.1016/j.physd.2014.09.002
ISSN:0167-2789 (print)
ISSN:1872-8022 (online)
Parent Title (English):Physica : D, Nonlinear phenomena
Publisher:Elsevier
Place of publication:Amsterdam
Document Type:Article
Language:English
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/26
Tag:Bi-harmonic coupling function; Kuramoto model; Multi-branch entrainment; Synchronization
Volume:289
Pagenumber:14
First Page:18
Last Page:31
Funder:Alexander von Humboldt Foundation; Ministry of Education and Science of the Russian Federation [02..49.21.0003]; Lobachevsky State University of Nizhni Novgorod [02..49.21.0003]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert