Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State

Detalhes bibliográficos
Autor(a) principal: Mahmoud, M. S.
Data de Publicação: 2023
Outros Autores: Medhat, M., Cerdeira, Hilda A. [UNESP], El-Nashar, Hassan F.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1142/S0218127423500050
http://hdl.handle.net/11449/248363
Resumo: We consider a Kuramoto model of four-coupled oscillators of nonidentical initial frequencies. Under the influence of coupling, the oscillators fall into a full phase locked state of a common frequency when the coupling strength surpasses a threshold value. We find numerically the parameters that control this distinguishable coupling constant at the moment the oscillators transit into an entire frequency synchronization when a complete phase lock state takes place. We are able to set apart a recognizable phase condition at the fully locked state. This phase condition helps to derive an analytic formula to calculate the coupling factor as soon as the oscillators depart to a full phase locking state. The explicit expression of the edge coupling factor is given in terms of the initial frequencies of the four oscillators. The formula valid for calculating the distinct coupling allows to find mathematical expressions to calculate the phase differences when the four-coupled phase oscillators are strictly at the full phase locked state and have a common frequency synchronization.
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spelling Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked Statecoupled phase oscillatorsFrequency synchronizationKuramoto modelWe consider a Kuramoto model of four-coupled oscillators of nonidentical initial frequencies. Under the influence of coupling, the oscillators fall into a full phase locked state of a common frequency when the coupling strength surpasses a threshold value. We find numerically the parameters that control this distinguishable coupling constant at the moment the oscillators transit into an entire frequency synchronization when a complete phase lock state takes place. We are able to set apart a recognizable phase condition at the fully locked state. This phase condition helps to derive an analytic formula to calculate the coupling factor as soon as the oscillators depart to a full phase locking state. The explicit expression of the edge coupling factor is given in terms of the initial frequencies of the four oscillators. The formula valid for calculating the distinct coupling allows to find mathematical expressions to calculate the phase differences when the four-coupled phase oscillators are strictly at the full phase locked state and have a common frequency synchronization.Department of Physics Faculty of Science Ain Shams University, AbassiaInstituto de Fisica Teorica Sao Paulo State University (UNESP), Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra FundaInstituto de Fisica Teorica Sao Paulo State University (UNESP), Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra FundaAin Shams UniversityUniversidade Estadual Paulista (UNESP)Mahmoud, M. S.Medhat, M.Cerdeira, Hilda A. [UNESP]El-Nashar, Hassan F.2023-07-29T13:41:55Z2023-07-29T13:41:55Z2023-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1142/S0218127423500050International Journal of Bifurcation and Chaos, v. 33, n. 1, 2023.0218-1274http://hdl.handle.net/11449/24836310.1142/S02181274235000502-s2.0-85148223523Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Bifurcation and Chaosinfo:eu-repo/semantics/openAccess2023-07-29T13:41:55Zoai:repositorio.unesp.br:11449/248363Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T13:41:55Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State
title Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State
spellingShingle Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State
Mahmoud, M. S.
coupled phase oscillators
Frequency synchronization
Kuramoto model
title_short Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State
title_full Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State
title_fullStr Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State
title_full_unstemmed Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State
title_sort Exact Solution of Four-Coupled Nonidentical Kuramoto Oscillators at a Full Phase Locked State
author Mahmoud, M. S.
author_facet Mahmoud, M. S.
Medhat, M.
Cerdeira, Hilda A. [UNESP]
El-Nashar, Hassan F.
author_role author
author2 Medhat, M.
Cerdeira, Hilda A. [UNESP]
El-Nashar, Hassan F.
author2_role author
author
author
dc.contributor.none.fl_str_mv Ain Shams University
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Mahmoud, M. S.
Medhat, M.
Cerdeira, Hilda A. [UNESP]
El-Nashar, Hassan F.
dc.subject.por.fl_str_mv coupled phase oscillators
Frequency synchronization
Kuramoto model
topic coupled phase oscillators
Frequency synchronization
Kuramoto model
description We consider a Kuramoto model of four-coupled oscillators of nonidentical initial frequencies. Under the influence of coupling, the oscillators fall into a full phase locked state of a common frequency when the coupling strength surpasses a threshold value. We find numerically the parameters that control this distinguishable coupling constant at the moment the oscillators transit into an entire frequency synchronization when a complete phase lock state takes place. We are able to set apart a recognizable phase condition at the fully locked state. This phase condition helps to derive an analytic formula to calculate the coupling factor as soon as the oscillators depart to a full phase locking state. The explicit expression of the edge coupling factor is given in terms of the initial frequencies of the four oscillators. The formula valid for calculating the distinct coupling allows to find mathematical expressions to calculate the phase differences when the four-coupled phase oscillators are strictly at the full phase locked state and have a common frequency synchronization.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-29T13:41:55Z
2023-07-29T13:41:55Z
2023-01-01
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/10.1142/S0218127423500050
International Journal of Bifurcation and Chaos, v. 33, n. 1, 2023.
0218-1274
http://hdl.handle.net/11449/248363
10.1142/S0218127423500050
2-s2.0-85148223523
url http://dx.doi.org/10.1142/S0218127423500050
http://hdl.handle.net/11449/248363
identifier_str_mv International Journal of Bifurcation and Chaos, v. 33, n. 1, 2023.
0218-1274
10.1142/S0218127423500050
2-s2.0-85148223523
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv International Journal of Bifurcation and Chaos
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_ 1799964702899437568

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