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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Main Authors: L A Smirnov, M I Bolotov, A Pikovsky
Format: Article
Language:English
Published: IOP Publishing 2024-01-01
Series:Journal of Physics: Complexity
Subjects:
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.
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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
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AT mibolotov nonuniformlytwistedstatesandtravelingchimerasinasystemofnonlocallycoupledidenticalphaseoscillators
AT apikovsky nonuniformlytwistedstatesandtravelingchimerasinasystemofnonlocallycoupledidenticalphaseoscillators