Periodic orbit bifurcations in planar hysteretic systems without equilibria

This paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from 3D systems with slow–fast dynamics. We focus our attention on the symmetric case without equilibria, determining the existence of periodic orbits as well as their stability, and possible bifur...

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Detalles Bibliográficos
Autores: Esteban, Marina, Ponce, Enrique, Torres, Francisco
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad Pablo de Olavide (UPO)
Repositorio:RIO. Repositorio Institucional Olavide
Idioma:inglés
OAI Identifier:oai:rio.upo.es:10433/22273
Acceso en línea:https://hdl.handle.net/10433/22273
Access Level:acceso abierto
Palabra clave:Bifurcation
Hysteresis
Periodic Orbit
Equilibrium
Planar Hysteretic System
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spelling Periodic orbit bifurcations in planar hysteretic systems without equilibriaEsteban, MarinaPonce, EnriqueTorres, FranciscoBifurcationHysteresisPeriodic OrbitEquilibriumPlanar Hysteretic SystemThis paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from 3D systems with slow–fast dynamics. We focus our attention on the symmetric case without equilibria, determining the existence of periodic orbits as well as their stability, and possible bifurcations. New analytical characterizations of bifurcations in these hysteretic systems are obtained. In particular, bifurcations of periodic orbits from infinity, grazing and saddle-node bifurcations of periodic orbits are studied in detail and the corresponding bifurcation sets are provided. Finally, the study of the hysteretic systems is shown to be useful in detecting periodic orbits for some 3D piecewise linear systems.World Scientific Publishing Company20252025-01-1420202020-07-1520202020-07-15journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10433/22273reponame:RIO. Repositorio Institucional Olavideinstname:Universidad Pablo de Olavide (UPO)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:rio.upo.es:10433/222732026-06-13T12:46:27Z
dc.title.none.fl_str_mv Periodic orbit bifurcations in planar hysteretic systems without equilibria
title Periodic orbit bifurcations in planar hysteretic systems without equilibria
spellingShingle Periodic orbit bifurcations in planar hysteretic systems without equilibria
Esteban, Marina
Bifurcation
Hysteresis
Periodic Orbit
Equilibrium
Planar Hysteretic System
title_short Periodic orbit bifurcations in planar hysteretic systems without equilibria
title_full Periodic orbit bifurcations in planar hysteretic systems without equilibria
title_fullStr Periodic orbit bifurcations in planar hysteretic systems without equilibria
title_full_unstemmed Periodic orbit bifurcations in planar hysteretic systems without equilibria
title_sort Periodic orbit bifurcations in planar hysteretic systems without equilibria
dc.creator.none.fl_str_mv Esteban, Marina
Ponce, Enrique
Torres, Francisco
author Esteban, Marina
author_facet Esteban, Marina
Ponce, Enrique
Torres, Francisco
author_role author
author2 Ponce, Enrique
Torres, Francisco
author2_role author
author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Bifurcation
Hysteresis
Periodic Orbit
Equilibrium
Planar Hysteretic System
topic Bifurcation
Hysteresis
Periodic Orbit
Equilibrium
Planar Hysteretic System
description This paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from 3D systems with slow–fast dynamics. We focus our attention on the symmetric case without equilibria, determining the existence of periodic orbits as well as their stability, and possible bifurcations. New analytical characterizations of bifurcations in these hysteretic systems are obtained. In particular, bifurcations of periodic orbits from infinity, grazing and saddle-node bifurcations of periodic orbits are studied in detail and the corresponding bifurcation sets are provided. Finally, the study of the hysteretic systems is shown to be useful in detecting periodic orbits for some 3D piecewise linear systems.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-07-15
2020
2020-07-15
2025
2025-01-14
dc.type.none.fl_str_mv journal 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://hdl.handle.net/10433/22273
url https://hdl.handle.net/10433/22273
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv World Scientific Publishing Company
publisher.none.fl_str_mv World Scientific Publishing Company
dc.source.none.fl_str_mv reponame:RIO. Repositorio Institucional Olavide
instname:Universidad Pablo de Olavide (UPO)
instname_str Universidad Pablo de Olavide (UPO)
reponame_str RIO. Repositorio Institucional Olavide
collection RIO. Repositorio Institucional Olavide
repository.name.fl_str_mv
repository.mail.fl_str_mv
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