Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators

Detalhes bibliográficos
Autor(a) principal: Barbi,Ivo
Data de Publicação: 2021
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100806
Resumo: This paper provides contributions to the study of the phase synchronization transient of two identical linear LC oscillators, coupled through a resistor. The main contribution is obtaining an exact equation that represents, as a function of time, the evolution of the phase angle between the two oscillators, from the initial condition until the synchronization. It is demonstrated that the system has two equilibrium points, one unstable when the phase angle is equal to π, and the other stable when it is equal to zero and to which the phase converges for any initial value other than π. It is also demonstrated that the dynamics of the two coupled oscillators can be described by the Kuramoto model. An analysis of the energy dissipated during synchronization is presented and the concept of synchronization energy is introduced. The results of the theoretical analysis are verified with the use of computer simulation.
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spelling Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillatorsCoupled oscillatorsKuramotolinear LC oscillatorsphase synchronization.This paper provides contributions to the study of the phase synchronization transient of two identical linear LC oscillators, coupled through a resistor. The main contribution is obtaining an exact equation that represents, as a function of time, the evolution of the phase angle between the two oscillators, from the initial condition until the synchronization. It is demonstrated that the system has two equilibrium points, one unstable when the phase angle is equal to π, and the other stable when it is equal to zero and to which the phase converges for any initial value other than π. It is also demonstrated that the dynamics of the two coupled oscillators can be described by the Kuramoto model. An analysis of the energy dissipated during synchronization is presented and the concept of synchronization energy is introduced. The results of the theoretical analysis are verified with the use of computer simulation.Sociedade Brasileira de Física2021-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100806Revista Brasileira de Ensino de Física v.43 2021reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2021-0126info:eu-repo/semantics/openAccessBarbi,Ivoeng2021-05-19T00:00:00Zoai:scielo:S1806-11172021000100806Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2021-05-19T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators
title Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators
spellingShingle Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators
Barbi,Ivo
Coupled oscillators
Kuramoto
linear LC oscillators
phase synchronization.
title_short Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators
title_full Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators
title_fullStr Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators
title_full_unstemmed Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators
title_sort Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators
author Barbi,Ivo
author_facet Barbi,Ivo
author_role author
dc.contributor.author.fl_str_mv Barbi,Ivo
dc.subject.por.fl_str_mv Coupled oscillators
Kuramoto
linear LC oscillators
phase synchronization.
topic Coupled oscillators
Kuramoto
linear LC oscillators
phase synchronization.
description This paper provides contributions to the study of the phase synchronization transient of two identical linear LC oscillators, coupled through a resistor. The main contribution is obtaining an exact equation that represents, as a function of time, the evolution of the phase angle between the two oscillators, from the initial condition until the synchronization. It is demonstrated that the system has two equilibrium points, one unstable when the phase angle is equal to π, and the other stable when it is equal to zero and to which the phase converges for any initial value other than π. It is also demonstrated that the dynamics of the two coupled oscillators can be described by the Kuramoto model. An analysis of the energy dissipated during synchronization is presented and the concept of synchronization energy is introduced. The results of the theoretical analysis are verified with the use of computer simulation.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100806
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100806
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1806-9126-rbef-2021-0126
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.43 2021
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
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instname_str Sociedade Brasileira de Física (SBF)
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institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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