Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones

Bibliographic Details
Main Author: Pessoa, Claudio [UNESP]
Publication Date: 2022
Other Authors: Ribeiro, Ronisio [UNESP]
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1142/S0218127422501140
http://hdl.handle.net/11449/241272
Summary: In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in a discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove that if the central subsystem, i.e. the system defined between the two parallel lines, has a real center and the other subsystems have centers or saddles, then we have at least three limit cycles that appear after perturbations of the periodic annulus. For this, we study the number of zeros of a Melnikov function for piecewise Hamiltonian system and present a normal form for this system in order to simplify the computations.
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spelling Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three ZonesLimit cyclesMelnikov functionPeriodic annulusPiecewise Hamiltonian differential systemIn this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in a discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove that if the central subsystem, i.e. the system defined between the two parallel lines, has a real center and the other subsystems have centers or saddles, then we have at least three limit cycles that appear after perturbations of the periodic annulus. For this, we study the number of zeros of a Melnikov function for piecewise Hamiltonian system and present a normal form for this system in order to simplify the computations.Departamento de Matemática IBILCE-UNESP, R. Cristovão Colombo 2265, S. J. Rio Preto, SPDepartamento de Matemática IBILCE-UNESP, R. Cristovão Colombo 2265, S. J. Rio Preto, SPUniversidade Estadual Paulista (UNESP)Pessoa, Claudio [UNESP]Ribeiro, Ronisio [UNESP]2023-03-01T20:54:33Z2023-03-01T20:54:33Z2022-06-30info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1142/S0218127422501140International Journal of Bifurcation and Chaos, v. 32, n. 8, 2022.0218-1274http://hdl.handle.net/11449/24127210.1142/S02181274225011402-s2.0-85133418641Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Bifurcation and Chaosinfo:eu-repo/semantics/openAccess2024-11-01T14:27:30Zoai:repositorio.unesp.br:11449/241272Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462024-11-01T14:27:30Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
title Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
spellingShingle Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
Pessoa, Claudio [UNESP]
Limit cycles
Melnikov function
Periodic annulus
Piecewise Hamiltonian differential system
title_short Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
title_full Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
title_fullStr Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
title_full_unstemmed Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
title_sort Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
author Pessoa, Claudio [UNESP]
author_facet Pessoa, Claudio [UNESP]
Ribeiro, Ronisio [UNESP]
author_role author
author2 Ribeiro, Ronisio [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Pessoa, Claudio [UNESP]
Ribeiro, Ronisio [UNESP]
dc.subject.por.fl_str_mv Limit cycles
Melnikov function
Periodic annulus
Piecewise Hamiltonian differential system
topic Limit cycles
Melnikov function
Periodic annulus
Piecewise Hamiltonian differential system
description In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in a discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove that if the central subsystem, i.e. the system defined between the two parallel lines, has a real center and the other subsystems have centers or saddles, then we have at least three limit cycles that appear after perturbations of the periodic annulus. For this, we study the number of zeros of a Melnikov function for piecewise Hamiltonian system and present a normal form for this system in order to simplify the computations.
publishDate 2022
dc.date.none.fl_str_mv 2022-06-30
2023-03-01T20:54:33Z
2023-03-01T20:54:33Z
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/S0218127422501140
International Journal of Bifurcation and Chaos, v. 32, n. 8, 2022.
0218-1274
http://hdl.handle.net/11449/241272
10.1142/S0218127422501140
2-s2.0-85133418641
url http://dx.doi.org/10.1142/S0218127422501140
http://hdl.handle.net/11449/241272
identifier_str_mv International Journal of Bifurcation and Chaos, v. 32, n. 8, 2022.
0218-1274
10.1142/S0218127422501140
2-s2.0-85133418641
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 repositoriounesp@unesp.br
_version_ 1834483839483772928

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