Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators
We explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 Phys. Rev. Lett. 93 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and as...
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Format: | Article |
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IOP Publishing
2024-01-01
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Series: | Journal of Physics: Complexity |
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Online Access: | https://doi.org/10.1088/2632-072X/ad2ec2 |
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author | L A Smirnov M I Bolotov A Pikovsky |
author_facet | L A Smirnov M I Bolotov A Pikovsky |
author_sort | L A Smirnov |
collection | DOAJ |
description | We explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 Phys. Rev. Lett. 93 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and asymmetric couplings. Only the simplest of these waves are stable, which is confirmed by numerical simulations for a finite population. We demonstrate that for asymmetric coupling, a weakly turbulent traveling chimera regime is established, both from an initial standing chimera or an unstable traveling wave profile. The weakly turbulent chimera is a macroscopically chaotic state, with a well-defined synchronous domain and partial coherence in the disordered domain. We characterize it through the correlation function and the Lyapunov spectrum. |
first_indexed | 2024-04-25T00:14:18Z |
format | Article |
id | doaj.art-2fc47dec02cf4b748993f886d4c05280 |
institution | Directory Open Access Journal |
issn | 2632-072X |
language | English |
last_indexed | 2024-04-25T00:14:18Z |
publishDate | 2024-01-01 |
publisher | IOP Publishing |
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series | Journal of Physics: Complexity |
spelling | doaj.art-2fc47dec02cf4b748993f886d4c052802024-03-13T05:41:17ZengIOP PublishingJournal of Physics: Complexity2632-072X2024-01-015101501910.1088/2632-072X/ad2ec2Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillatorsL A Smirnov0https://orcid.org/0000-0002-2293-6534M I Bolotov1https://orcid.org/0000-0001-9561-2357A Pikovsky2https://orcid.org/0000-0001-9682-7122Department of Control Theory, Research and Education Mathematical Center ‘Mathematics for Future Technologies’, Nizhny Novgorod State University , Gagarin Av. 23, 603022 Nizhny Novgorod, RussiaDepartment of Control Theory, Research and Education Mathematical Center ‘Mathematics for Future Technologies’, Nizhny Novgorod State University , Gagarin Av. 23, 603022 Nizhny Novgorod, RussiaDepartment of Physics and Astronomy, University of Potsdam , Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, GermanyWe explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 Phys. Rev. Lett. 93 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and asymmetric couplings. Only the simplest of these waves are stable, which is confirmed by numerical simulations for a finite population. We demonstrate that for asymmetric coupling, a weakly turbulent traveling chimera regime is established, both from an initial standing chimera or an unstable traveling wave profile. The weakly turbulent chimera is a macroscopically chaotic state, with a well-defined synchronous domain and partial coherence in the disordered domain. We characterize it through the correlation function and the Lyapunov spectrum.https://doi.org/10.1088/2632-072X/ad2ec2twisted statestraveling chimeraphase oscillatorsLyapunov exponentnonlocal couplingasymmetric coupling |
spellingShingle | L A Smirnov M I Bolotov A Pikovsky Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators Journal of Physics: Complexity twisted states traveling chimera phase oscillators Lyapunov exponent nonlocal coupling asymmetric coupling |
title | Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators |
title_full | Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators |
title_fullStr | Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators |
title_full_unstemmed | Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators |
title_short | Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators |
title_sort | nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators |
topic | twisted states traveling chimera phase oscillators Lyapunov exponent nonlocal coupling asymmetric coupling |
url | https://doi.org/10.1088/2632-072X/ad2ec2 |
work_keys_str_mv | AT lasmirnov nonuniformlytwistedstatesandtravelingchimerasinasystemofnonlocallycoupledidenticalphaseoscillators AT mibolotov nonuniformlytwistedstatesandtravelingchimerasinasystemofnonlocallycoupledidenticalphaseoscillators AT apikovsky nonuniformlytwistedstatesandtravelingchimerasinasystemofnonlocallycoupledidenticalphaseoscillators |