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Regular and Chaotic Dynamics, 2019, Volume 24, Issue 6, Pages 717–724
DOI: https://doi.org/10.1134/S1560354719060091 (Mi rcd1035) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Twisted States in a System of Nonlinearly Coupled Phase Oscillators

Dmitry Bolotova, Maxim Bolotova, Lev Smirnovab, Grigory Osipova, Arkady Pikovskyca

a Department of Control Theory, Nizhny Novgorod State University, pr. Gagarina 23, Nizhny Novgorod, 603950 Russia
b Institute of Applied Physics, Russian Academy of Sciences, ul. Ul’yanova 46, Nizhny Novgorod, 603950 Russia
c Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24-25, 14476 Potsdam, Germany
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DOI: https://doi.org/10.1134/S1560354719060091
Abstract: We study the dynamics of the ring of identical phase oscillators with nonlinear nonlocal coupling. Using the Ott – Antonsen approach, the problem is formulated as a system of partial derivative equations for the local complex order parameter. In this framework, we investigate the existence and stability of twisted states. Both fully coherent and partially coherent stable twisted states were found (the latter ones for the first time for identical oscillators). We show that twisted states can be stable starting from a certain critical value of the medium length, or on a length segment. The analytical results are confirmed with direct numerical simulations in finite ensembles.
Keywords: twisted state, phase oscillators, nonlocal coupling, Ott – Antonsen reduction, stability analysis.
Funding agency Grant number
Russian Foundation for Basic Research 19-52-12053
Russian Science Foundation 19-12-00367
This work was supported by the RFBR (grant No. 19-52-12053) and the RSF (grant No. 19-12-00367).
Received: 23.10.2019
Accepted: 10.11.2019
Bibliographic databases:
Document Type: Article
MSC: 34C15
Language: English
Citation: Dmitry Bolotov, Maxim Bolotov, Lev Smirnov, Grigory Osipov, Arkady Pikovsky, “Twisted States in a System of Nonlinearly Coupled Phase Oscillators”, Regul. Chaotic Dyn., 24:6 (2019), 717–724
Citation in format AMSBIB
\Bibitem{BolBolSmi19}
\by Dmitry Bolotov, Maxim Bolotov, Lev Smirnov, Grigory Osipov, Arkady Pikovsky
\paper Twisted States in a System of Nonlinearly Coupled Phase Oscillators
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 6
\pages 717--724
\mathnet{http://mi.mathnet.ru/rcd1035}
\crossref{https://doi.org/10.1134/S1560354719060091}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85076350324}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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