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.
| Author details: | Maxim Komarov, Arkadij PikovskijORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1016/j.physd.2014.09.002 |
| ISSN: | 0167-2789 |
| ISSN: | 1872-8022 |
| Title of parent work (English): | Physica : D, Nonlinear phenomena |
| Publisher: | Elsevier |
| Place of publishing: | Amsterdam |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2014 |
| Publication year: | 2014 |
| Release date: | 2017/03/26 |
| Tag: | Bi-harmonic coupling function; Kuramoto model; Multi-branch entrainment; Synchronization |
| Volume: | 289 |
| Number of pages: | 14 |
| First page: | 18 |
| Last Page: | 31 |
| Funding institution: | 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 |
