Center boundaries for planar piecewise-smooth differential equations with two zones

This paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system,...

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Autores: Buzzi, Claudio.|||0000-0003-2037-8417, Pazim, Rubens, Pérez-González, Set|||0000-0002-1522-7086
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:182517
Acceso en línea:https://ddd.uab.cat/record/182517
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2016.07.022
Access Level:acceso abierto
Palabra clave:Limit cycles
Non-smooth differential systems
Piecewise linear differential system
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spelling Center boundaries for planar piecewise-smooth differential equations with two zonesBuzzi, Claudio.|||0000-0003-2037-8417Pazim, RubensPérez-González, Set|||0000-0002-1522-7086Limit cyclesNon-smooth differential systemsPiecewise linear differential systemThis paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system, formed by the pair of smooth systems, has a continuum of periodic orbits. In this case we call the separation boundary as a center boundary. We prove that given a pair of systems that share a hyperbolic focus singularity p 0 , with the same orientation and opposite stability, and a ray Σ 0 with endpoint at the singularity p 0 , we can find a smooth manifold Ω such that Σ 0 ∪ p 0 ∪ Ω is a center boundary. The maximum number of such manifolds satisfying these conditions is five. Moreover, this upper bound is reached. 22017-01-0120172017-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/182517https://dx.doi.org/urn:doi:10.1016/j.jmaa.2016.07.022reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengEuropean Commission https://doi.org/10.13039/501100000780 318999open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1825172026-06-06T12:50:31Z
dc.title.none.fl_str_mv Center boundaries for planar piecewise-smooth differential equations with two zones
title Center boundaries for planar piecewise-smooth differential equations with two zones
spellingShingle Center boundaries for planar piecewise-smooth differential equations with two zones
Buzzi, Claudio.|||0000-0003-2037-8417
Limit cycles
Non-smooth differential systems
Piecewise linear differential system
title_short Center boundaries for planar piecewise-smooth differential equations with two zones
title_full Center boundaries for planar piecewise-smooth differential equations with two zones
title_fullStr Center boundaries for planar piecewise-smooth differential equations with two zones
title_full_unstemmed Center boundaries for planar piecewise-smooth differential equations with two zones
title_sort Center boundaries for planar piecewise-smooth differential equations with two zones
dc.creator.none.fl_str_mv Buzzi, Claudio.|||0000-0003-2037-8417
Pazim, Rubens
Pérez-González, Set|||0000-0002-1522-7086
author Buzzi, Claudio.|||0000-0003-2037-8417
author_facet Buzzi, Claudio.|||0000-0003-2037-8417
Pazim, Rubens
Pérez-González, Set|||0000-0002-1522-7086
author_role author
author2 Pazim, Rubens
Pérez-González, Set|||0000-0002-1522-7086
author2_role author
author
dc.subject.none.fl_str_mv Limit cycles
Non-smooth differential systems
Piecewise linear differential system
topic Limit cycles
Non-smooth differential systems
Piecewise linear differential system
description This paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system, formed by the pair of smooth systems, has a continuum of periodic orbits. In this case we call the separation boundary as a center boundary. We prove that given a pair of systems that share a hyperbolic focus singularity p 0 , with the same orientation and opposite stability, and a ray Σ 0 with endpoint at the singularity p 0 , we can find a smooth manifold Ω such that Σ 0 ∪ p 0 ∪ Ω is a center boundary. The maximum number of such manifolds satisfying these conditions is five. Moreover, this upper bound is reached.
publishDate 2017
dc.date.none.fl_str_mv 2
2017-01-01
2017
2017-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/182517
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2016.07.022
url https://ddd.uab.cat/record/182517
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2016.07.022
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission https://doi.org/10.13039/501100000780 318999
dc.rights.none.fl_str_mv open access
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https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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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
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