Basin sizes depend on stable eigenvalues in the Kuramoto model

Detalhes bibliográficos
Autor(a) principal: Mihara, Antonio
Data de Publicação: 2022
Outros Autores: Zaks, Michael, Macau, Elbert E. N., Medrano-T, Rene O. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1103/PhysRevE.105.L052202
http://hdl.handle.net/11449/241120
Resumo: We show that for the Kuramoto model (with identical phase oscillators equally coupled), its global statistics and size of the basins of attraction can be estimated through the eigenvalues of all stable (frequency) synchronized states. This result is somehow unexpected since, by doing that, one could just use a local analysis to obtain the global dynamic properties. But recent works based on Koopman and Perron-Frobenius operators demonstrate that the global features of a nonlinear dynamical system, with some specific conditions, are somehow encoded in the local eigenvalues of its equilibrium states. Recognized numerical simulations in the literature reinforce our analytical results.
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spelling Basin sizes depend on stable eigenvalues in the Kuramoto modelWe show that for the Kuramoto model (with identical phase oscillators equally coupled), its global statistics and size of the basins of attraction can be estimated through the eigenvalues of all stable (frequency) synchronized states. This result is somehow unexpected since, by doing that, one could just use a local analysis to obtain the global dynamic properties. But recent works based on Koopman and Perron-Frobenius operators demonstrate that the global features of a nonlinear dynamical system, with some specific conditions, are somehow encoded in the local eigenvalues of its equilibrium states. Recognized numerical simulations in the literature reinforce our analytical results.Departamento de Física Universidade Federal de São Paulo UNIFESP Campus DiademaInstitute of Physics Humboldt University of BerlinUniversidade Federal de São Paulo UNIFESP Campus São José Dos CamposDepartamento de Física Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista UNESP Campus Rio ClaroDepartamento de Física Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista UNESP Campus Rio ClaroUniversidade Federal de São Paulo (UNIFESP)Humboldt University of BerlinUniversidade Estadual Paulista (UNESP)Mihara, AntonioZaks, MichaelMacau, Elbert E. N.Medrano-T, Rene O. [UNESP]2023-03-01T20:48:03Z2023-03-01T20:48:03Z2022-05-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.105.L052202Physical Review E, v. 105, n. 5, 2022.2470-00532470-0045http://hdl.handle.net/11449/24112010.1103/PhysRevE.105.L0522022-s2.0-85131460097Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Einfo:eu-repo/semantics/openAccess2023-03-01T20:48:03Zoai:repositorio.unesp.br:11449/241120Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:44:42.269291Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Basin sizes depend on stable eigenvalues in the Kuramoto model
title Basin sizes depend on stable eigenvalues in the Kuramoto model
spellingShingle Basin sizes depend on stable eigenvalues in the Kuramoto model
Mihara, Antonio
title_short Basin sizes depend on stable eigenvalues in the Kuramoto model
title_full Basin sizes depend on stable eigenvalues in the Kuramoto model
title_fullStr Basin sizes depend on stable eigenvalues in the Kuramoto model
title_full_unstemmed Basin sizes depend on stable eigenvalues in the Kuramoto model
title_sort Basin sizes depend on stable eigenvalues in the Kuramoto model
author Mihara, Antonio
author_facet Mihara, Antonio
Zaks, Michael
Macau, Elbert E. N.
Medrano-T, Rene O. [UNESP]
author_role author
author2 Zaks, Michael
Macau, Elbert E. N.
Medrano-T, Rene O. [UNESP]
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Federal de São Paulo (UNIFESP)
Humboldt University of Berlin
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Mihara, Antonio
Zaks, Michael
Macau, Elbert E. N.
Medrano-T, Rene O. [UNESP]
description We show that for the Kuramoto model (with identical phase oscillators equally coupled), its global statistics and size of the basins of attraction can be estimated through the eigenvalues of all stable (frequency) synchronized states. This result is somehow unexpected since, by doing that, one could just use a local analysis to obtain the global dynamic properties. But recent works based on Koopman and Perron-Frobenius operators demonstrate that the global features of a nonlinear dynamical system, with some specific conditions, are somehow encoded in the local eigenvalues of its equilibrium states. Recognized numerical simulations in the literature reinforce our analytical results.
publishDate 2022
dc.date.none.fl_str_mv 2022-05-01
2023-03-01T20:48:03Z
2023-03-01T20:48:03Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1103/PhysRevE.105.L052202
Physical Review E, v. 105, n. 5, 2022.
2470-0053
2470-0045
http://hdl.handle.net/11449/241120
10.1103/PhysRevE.105.L052202
2-s2.0-85131460097
url http://dx.doi.org/10.1103/PhysRevE.105.L052202
http://hdl.handle.net/11449/241120
identifier_str_mv Physical Review E, v. 105, n. 5, 2022.
2470-0053
2470-0045
10.1103/PhysRevE.105.L052202
2-s2.0-85131460097
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physical Review E
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129112634556416

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