Effective construction of Poincaré-Bendixson regions

This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically dete...

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Detalles Bibliográficos
Autores: Gasull, Armengol, Giacomini, Héctor, Grau Montaña, Maite
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/60471
Acceso en línea:https://doi.org/10.11948/2017094
http://hdl.handle.net/10459.1/60471
Access Level:acceso abierto
Palabra clave:Transversal curve
Poincaré-Bendixson region
Limit cycle
Bifurcation
Planar differential system
Matemàtica
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spelling Effective construction of Poincaré-Bendixson regionsGasull, ArmengolGiacomini, HéctorGrau Montaña, MaiteTransversal curvePoincaré-Bendixson regionLimit cycleBifurcationPlanar differential systemMatemàticaThis paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically detected. We apply our results to several known systems, like the Brusselator one or some Liénard systems, to prove the existence of the limit cycles and to locate them very precisely in the phase space. Our method, combined with some other classical tools can be applied to obtain sharp bounds for the bifurcation values of a saddle-node bifurcation of limit cycles, as we do for the Rychkov system.Shanghai Normal University & Wilmington Scientific Publisher2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.11948/2017094http://hdl.handle.net/10459.1/60471reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésReproducció del document publicat a: https://doi.org/10.11948/2017094Journal Of Applied Analysis And Computation, 2017, vol. 7, núm. 4, p. 1549-1569cc-by (c) Gasull et al., 2017info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/oai:repositori.udl.cat:10459.1/604712026-06-24T12:42:17Z
dc.title.none.fl_str_mv Effective construction of Poincaré-Bendixson regions
title Effective construction of Poincaré-Bendixson regions
spellingShingle Effective construction of Poincaré-Bendixson regions
Gasull, Armengol
Transversal curve
Poincaré-Bendixson region
Limit cycle
Bifurcation
Planar differential system
Matemàtica
title_short Effective construction of Poincaré-Bendixson regions
title_full Effective construction of Poincaré-Bendixson regions
title_fullStr Effective construction of Poincaré-Bendixson regions
title_full_unstemmed Effective construction of Poincaré-Bendixson regions
title_sort Effective construction of Poincaré-Bendixson regions
dc.creator.none.fl_str_mv Gasull, Armengol
Giacomini, Héctor
Grau Montaña, Maite
author Gasull, Armengol
author_facet Gasull, Armengol
Giacomini, Héctor
Grau Montaña, Maite
author_role author
author2 Giacomini, Héctor
Grau Montaña, Maite
author2_role author
author
dc.subject.none.fl_str_mv Transversal curve
Poincaré-Bendixson region
Limit cycle
Bifurcation
Planar differential system
Matemàtica
topic Transversal curve
Poincaré-Bendixson region
Limit cycle
Bifurcation
Planar differential system
Matemàtica
description This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically detected. We apply our results to several known systems, like the Brusselator one or some Liénard systems, to prove the existence of the limit cycles and to locate them very precisely in the phase space. Our method, combined with some other classical tools can be applied to obtain sharp bounds for the bifurcation values of a saddle-node bifurcation of limit cycles, as we do for the Rychkov system.
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.11948/2017094
http://hdl.handle.net/10459.1/60471
url https://doi.org/10.11948/2017094
http://hdl.handle.net/10459.1/60471
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.11948/2017094
Journal Of Applied Analysis And Computation, 2017, vol. 7, núm. 4, p. 1549-1569
dc.rights.none.fl_str_mv cc-by (c) Gasull et al., 2017
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
rights_invalid_str_mv cc-by (c) Gasull et al., 2017
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Shanghai Normal University & Wilmington Scientific Publisher
publisher.none.fl_str_mv Shanghai Normal University & Wilmington Scientific Publisher
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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