Analytical approach to synchronous states of globally coupled noisy rotators
We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ab6f93 |
| _version_ | 1827873041334403072 |
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| author | V O Munyaev L A Smirnov V A Kostin G V Osipov A Pikovsky |
| author_facet | V O Munyaev L A Smirnov V A Kostin G V Osipov A Pikovsky |
| author_sort | V O Munyaev |
| collection | DOAJ |
| description | We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker–Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed. |
| first_indexed | 2024-03-12T16:31:55Z |
| format | Article |
| id | doaj.art-d88eb647c4e34c139d4d3f83e135ebe6 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:31:55Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-d88eb647c4e34c139d4d3f83e135ebe62023-08-08T15:28:51ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122202303610.1088/1367-2630/ab6f93Analytical approach to synchronous states of globally coupled noisy rotatorsV O Munyaev0https://orcid.org/0000-0002-8997-2898L A Smirnov1https://orcid.org/0000-0002-2293-6534V A Kostin2https://orcid.org/0000-0002-4720-943XG V Osipov3https://orcid.org/0000-0003-2841-8399A Pikovsky4https://orcid.org/0000-0001-9682-7122Department of Control Theory, Nizhny Novgorod State University , Gagarin Av. 23, Nizhny Novgorod, 603950, RussiaDepartment of Control Theory, Nizhny Novgorod State University , Gagarin Av. 23, Nizhny Novgorod, 603950, Russia; Institute of Applied Physics, Russian Academy of Sciences, Ul’yanova Str. 46, Nizhny Novgorod, 603950, RussiaDepartment of Control Theory, Nizhny Novgorod State University , Gagarin Av. 23, Nizhny Novgorod, 603950, Russia; Institute of Applied Physics, Russian Academy of Sciences, Ul’yanova Str. 46, Nizhny Novgorod, 603950, RussiaDepartment of Control Theory, Nizhny Novgorod State University , Gagarin Av. 23, Nizhny Novgorod, 603950, RussiaDepartment of Control Theory, Nizhny Novgorod State University , Gagarin Av. 23, Nizhny Novgorod, 603950, Russia; Institute for Physics and Astronomy, University of Potsdam , Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, GermanyWe study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker–Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.https://doi.org/10.1088/1367-2630/ab6f93coupled rotatorssynchronization transitionhysteresisKuramoto modelnoisy systems |
| spellingShingle | V O Munyaev L A Smirnov V A Kostin G V Osipov A Pikovsky Analytical approach to synchronous states of globally coupled noisy rotators New Journal of Physics coupled rotators synchronization transition hysteresis Kuramoto model noisy systems |
| title | Analytical approach to synchronous states of globally coupled noisy rotators |
| title_full | Analytical approach to synchronous states of globally coupled noisy rotators |
| title_fullStr | Analytical approach to synchronous states of globally coupled noisy rotators |
| title_full_unstemmed | Analytical approach to synchronous states of globally coupled noisy rotators |
| title_short | Analytical approach to synchronous states of globally coupled noisy rotators |
| title_sort | analytical approach to synchronous states of globally coupled noisy rotators |
| topic | coupled rotators synchronization transition hysteresis Kuramoto model noisy systems |
| url | https://doi.org/10.1088/1367-2630/ab6f93 |
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