Simultaneous Bifurcation of Limit Cycles and Critical Periods

The present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane. The simultaneity concept is defined, as well as the idea of bi-weakness in the return map and the period function. Together with th...

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Autores: Oliveira, Regilene|||0000-0002-9628-5180, Sanchez Sanchez, Ivan|||0000-0002-4534-3870, Torregrosa, Joan|||0000-0002-2753-1827
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:250628
Acceso en línea:https://ddd.uab.cat/record/250628
https://dx.doi.org/urn:doi:10.1007/s12346-021-00546-x
Access Level:acceso abierto
Palabra clave:Limit cycles
Critical periods
Simultaneous bifurcation
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spelling Simultaneous Bifurcation of Limit Cycles and Critical PeriodsOliveira, Regilene|||0000-0002-9628-5180Sanchez Sanchez, Ivan|||0000-0002-4534-3870Torregrosa, Joan|||0000-0002-2753-1827Limit cyclesCritical periodsSimultaneous bifurcationThe present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane. The simultaneity concept is defined, as well as the idea of bi-weakness in the return map and the period function. Together with the classical methods, we present an approach which uses the Lie bracket to address the simultaneity in some cases. This approach is used to find the bi-weakness of cubic and quartic Liénard systems, the general quadratic family, and the linear plus cubic homogeneous family. We finish with an illustrative example by solving the problem of simultaneous bifurcation of limit cycles and critical periods for the cubic Liénard family. 22022-01-0120222022-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/250628https://dx.doi.org/urn:doi:10.1007/s12346-021-00546-xreponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00Ministerio de Educación, Cultura y Deporte https://doi.org/10.13039/501100003176 FPU16/04317Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 CEX2020-001084-MAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617European Commission https://doi.org/10.13039/501100000780 777911open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2506282026-06-06T12:50:31Z
dc.title.none.fl_str_mv Simultaneous Bifurcation of Limit Cycles and Critical Periods
title Simultaneous Bifurcation of Limit Cycles and Critical Periods
spellingShingle Simultaneous Bifurcation of Limit Cycles and Critical Periods
Oliveira, Regilene|||0000-0002-9628-5180
Limit cycles
Critical periods
Simultaneous bifurcation
title_short Simultaneous Bifurcation of Limit Cycles and Critical Periods
title_full Simultaneous Bifurcation of Limit Cycles and Critical Periods
title_fullStr Simultaneous Bifurcation of Limit Cycles and Critical Periods
title_full_unstemmed Simultaneous Bifurcation of Limit Cycles and Critical Periods
title_sort Simultaneous Bifurcation of Limit Cycles and Critical Periods
dc.creator.none.fl_str_mv Oliveira, Regilene|||0000-0002-9628-5180
Sanchez Sanchez, Ivan|||0000-0002-4534-3870
Torregrosa, Joan|||0000-0002-2753-1827
author Oliveira, Regilene|||0000-0002-9628-5180
author_facet Oliveira, Regilene|||0000-0002-9628-5180
Sanchez Sanchez, Ivan|||0000-0002-4534-3870
Torregrosa, Joan|||0000-0002-2753-1827
author_role author
author2 Sanchez Sanchez, Ivan|||0000-0002-4534-3870
Torregrosa, Joan|||0000-0002-2753-1827
author2_role author
author
dc.subject.none.fl_str_mv Limit cycles
Critical periods
Simultaneous bifurcation
topic Limit cycles
Critical periods
Simultaneous bifurcation
description The present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane. The simultaneity concept is defined, as well as the idea of bi-weakness in the return map and the period function. Together with the classical methods, we present an approach which uses the Lie bracket to address the simultaneity in some cases. This approach is used to find the bi-weakness of cubic and quartic Liénard systems, the general quadratic family, and the linear plus cubic homogeneous family. We finish with an illustrative example by solving the problem of simultaneous bifurcation of limit cycles and critical periods for the cubic Liénard family.
publishDate 2022
dc.date.none.fl_str_mv 2
2022-01-01
2022
2022-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/250628
https://dx.doi.org/urn:doi:10.1007/s12346-021-00546-x
url https://ddd.uab.cat/record/250628
https://dx.doi.org/urn:doi:10.1007/s12346-021-00546-x
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00
Ministerio de Educación, Cultura y Deporte https://doi.org/10.13039/501100003176 FPU16/04317
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 CEX2020-001084-M
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
European Commission https://doi.org/10.13039/501100000780 777911
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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repository.mail.fl_str_mv
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