Bistable boundary conditions implying codimension 2 bifurcations

We consider generic families Xθ of smooth dynamical systems depending on parameters θ ∈ P where P is a 2-dimensional simply connected domain and assume that each Xθ only has a finite number of restpoints and periodic orbits. We prove that if over the boundary of P there is a S or Z shaped bifurcatio...

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Detalhes bibliográficos
Autores: Rand, David, Saez, Meritxell
Formato: artículo
Fecha de publicación:2025
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:20.500.14342/5202
Acesso em linha:http://hdl.handle.net/20.500.14342/5202
https://doi.org/10.1088/1361-6544/adb5e9
Access Level:acceso abierto
Palavra-chave:Dynamical systems
Bifurcations
Catastrophes
Cusp bifurcation
Bogdanov-Takens bifurcation
Dinàmica
Bifurcació, Teoria de la
Catàstrofes (Matemàtica)
51
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spelling Bistable boundary conditions implying codimension 2 bifurcationsRand, DavidSaez, MeritxellDynamical systemsBifurcationsCatastrophesCusp bifurcationBogdanov-Takens bifurcationDinàmicaBifurcació, Teoria de laCatàstrofes (Matemàtica)51We consider generic families Xθ of smooth dynamical systems depending on parameters θ ∈ P where P is a 2-dimensional simply connected domain and assume that each Xθ only has a finite number of restpoints and periodic orbits. We prove that if over the boundary of P there is a S or Z shaped bifurcation graph containing two opposing fold bifurcation points while over the rest of the boundary there are no other bifurcation points, then, if there is no fold-Hopf bifurcation in P, there is a set of bifurcation curves in P that contain an odd number of cusps. In particular, there is at least one codimension 2 bifurcation point in the interior of P.info:eu-repo/semantics/publishedVersionIOP Publishing i London Mathematical SocietyUniversitat Ramon Llull. IQS2025info:eu-repo/semantics/articlep.14http://hdl.handle.net/20.500.14342/5202https://doi.org/10.1088/1361-6544/adb5e9reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésNonlinearity 2025, 38© L'autor/aAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:20.500.14342/52022026-05-29T05:05:01Z
dc.title.none.fl_str_mv Bistable boundary conditions implying codimension 2 bifurcations
title Bistable boundary conditions implying codimension 2 bifurcations
spellingShingle Bistable boundary conditions implying codimension 2 bifurcations
Rand, David
Dynamical systems
Bifurcations
Catastrophes
Cusp bifurcation
Bogdanov-Takens bifurcation
Dinàmica
Bifurcació, Teoria de la
Catàstrofes (Matemàtica)
51
title_short Bistable boundary conditions implying codimension 2 bifurcations
title_full Bistable boundary conditions implying codimension 2 bifurcations
title_fullStr Bistable boundary conditions implying codimension 2 bifurcations
title_full_unstemmed Bistable boundary conditions implying codimension 2 bifurcations
title_sort Bistable boundary conditions implying codimension 2 bifurcations
dc.creator.none.fl_str_mv Rand, David
Saez, Meritxell
author Rand, David
author_facet Rand, David
Saez, Meritxell
author_role author
author2 Saez, Meritxell
author2_role author
dc.contributor.none.fl_str_mv Universitat Ramon Llull. IQS
dc.subject.none.fl_str_mv Dynamical systems
Bifurcations
Catastrophes
Cusp bifurcation
Bogdanov-Takens bifurcation
Dinàmica
Bifurcació, Teoria de la
Catàstrofes (Matemàtica)
51
topic Dynamical systems
Bifurcations
Catastrophes
Cusp bifurcation
Bogdanov-Takens bifurcation
Dinàmica
Bifurcació, Teoria de la
Catàstrofes (Matemàtica)
51
description We consider generic families Xθ of smooth dynamical systems depending on parameters θ ∈ P where P is a 2-dimensional simply connected domain and assume that each Xθ only has a finite number of restpoints and periodic orbits. We prove that if over the boundary of P there is a S or Z shaped bifurcation graph containing two opposing fold bifurcation points while over the rest of the boundary there are no other bifurcation points, then, if there is no fold-Hopf bifurcation in P, there is a set of bifurcation curves in P that contain an odd number of cusps. In particular, there is at least one codimension 2 bifurcation point in the interior of P.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.14342/5202
https://doi.org/10.1088/1361-6544/adb5e9
url http://hdl.handle.net/20.500.14342/5202
https://doi.org/10.1088/1361-6544/adb5e9
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinearity 2025, 38
dc.rights.none.fl_str_mv © L'autor/a
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © L'autor/a
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv p.14
dc.publisher.none.fl_str_mv IOP Publishing i London Mathematical Society
publisher.none.fl_str_mv IOP Publishing i London Mathematical Society
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869418293935210496
score 15.81155

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