Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability
- As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations.
Author details: | Vladimir Vlasov, Michael RosenblumORCiDGND, Arkadij PikovskijORCiDGND |
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DOI: | https://doi.org/10.1088/1751-8113/49/31/31LT02 |
ISSN: | 1751-8113 |
ISSN: | 1751-8121 |
Title of parent work (English): | Journal of physics : A, Mathematical and theoretical |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Year of first publication: | 2016 |
Publication year: | 2016 |
Release date: | 2020/03/22 |
Tag: | Kuramoto model; integrability; oscillator populations; perturbation theory |
Volume: | 49 |
Number of pages: | 8 |
Funding institution: | Russian Science Foundation [14-12-00811]; DFG /FAPESP [IRTG 1740/TRP 2011/50151-0] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |