Transition to collective oscillations in finite Kuramoto ensembles
- We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this purpose, the minimal value of the amplitude of the complex Kuramoto order parameter appears as a proper indicator. The dependence of this minimum on coupling strength varies due to sampling variations and correlates with the sample kurtosis of the natural frequency distribution. The skewness of the frequency sample determines the frequency of the resulting collective mode. The effects of kurtosis and skewness hold in the thermodynamic limit of infinite ensembles. We prove this by integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively.
Author details: | Franziska PeterORCiDGND, Arkadij PikovskijORCiDGND |
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DOI: | https://doi.org/10.1103/PhysRevE.97.032310 |
ISSN: | 2470-0045 |
ISSN: | 2470-0053 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/29776135 |
Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
Publisher: | American Physical Society |
Place of publishing: | College Park |
Publication type: | Article |
Language: | English |
Date of first publication: | 2018/03/20 |
Publication year: | 2018 |
Release date: | 2022/01/05 |
Volume: | 97 |
Issue: | 3 |
Number of pages: | 10 |
Funding institution: | DFG/FAPESP [IRTG 1740/TRP 2015/50122-0]; Russian Science FoundationRussian Science Foundation (RSF) [17-12-01534] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 52 Astronomie / 520 Astronomie und zugeordnete Wissenschaften |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |