Dynamics of oscillators globally coupled via two mean fields

Abstract Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean fields. We derive stability properties of the incoheren...

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Autores principales:	Xiyun Zhang, Arkady Pikovsky, Zonghua Liu
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/80e582005ed54fc6af082a903164eb9c
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spelling	oai:doaj.org-article:80e582005ed54fc6af082a903164eb9c2021-12-02T12:31:49ZDynamics of oscillators globally coupled via two mean fields10.1038/s41598-017-02283-12045-2322https://doaj.org/article/80e582005ed54fc6af082a903164eb9c2017-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-02283-1https://doaj.org/toc/2045-2322Abstract Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean fields. We derive stability properties of the incoherent state and find traveling wave solutions with different locking patterns; stability properties of these waves are found numerically. Mostly nontrivial states appear when the two fields compete, i.e. one tends to synchronize oscillators while the other one desynchronizes them. Here we identify normal branches which bifurcate from the incoherent state in a usual way, and anomalous branches, appearance of which cannot be described as a bifurcation. Furthermore, hybrid branches combining properties of both are described. In the situations where no stable traveling wave exists, modulated quasiperiodic in time dynamics is observed. Our results indicate that a competition between two coupling channels can lead to a complex system behavior, providing a potential generalized framework for understanding of complex phenomena in natural oscillatory systems.Xiyun ZhangArkady PikovskyZonghua LiuNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-16 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Xiyun Zhang Arkady Pikovsky Zonghua Liu Dynamics of oscillators globally coupled via two mean fields
description	Abstract Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean fields. We derive stability properties of the incoherent state and find traveling wave solutions with different locking patterns; stability properties of these waves are found numerically. Mostly nontrivial states appear when the two fields compete, i.e. one tends to synchronize oscillators while the other one desynchronizes them. Here we identify normal branches which bifurcate from the incoherent state in a usual way, and anomalous branches, appearance of which cannot be described as a bifurcation. Furthermore, hybrid branches combining properties of both are described. In the situations where no stable traveling wave exists, modulated quasiperiodic in time dynamics is observed. Our results indicate that a competition between two coupling channels can lead to a complex system behavior, providing a potential generalized framework for understanding of complex phenomena in natural oscillatory systems.
format	article
author	Xiyun Zhang Arkady Pikovsky Zonghua Liu
author_facet	Xiyun Zhang Arkady Pikovsky Zonghua Liu
author_sort	Xiyun Zhang
title	Dynamics of oscillators globally coupled via two mean fields
title_short	Dynamics of oscillators globally coupled via two mean fields
title_full	Dynamics of oscillators globally coupled via two mean fields
title_fullStr	Dynamics of oscillators globally coupled via two mean fields
title_full_unstemmed	Dynamics of oscillators globally coupled via two mean fields
title_sort	dynamics of oscillators globally coupled via two mean fields
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/80e582005ed54fc6af082a903164eb9c
work_keys_str_mv	AT xiyunzhang dynamicsofoscillatorsgloballycoupledviatwomeanfields AT arkadypikovsky dynamicsofoscillatorsgloballycoupledviatwomeanfields AT zonghualiu dynamicsofoscillatorsgloballycoupledviatwomeanfields
_version_	1718394287975038976

Dynamics of oscillators globally coupled via two mean fields

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