Slow–fast systems and sliding on codimension 2 switching manifolds
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1080/14689367.2019.1579782 http://hdl.handle.net/11449/188805 |
Resumo: | In this work, we consider piecewise smooth vector fields X defined in R n \ ∑, where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields X ε.η , ε,η > 0 satisfying that X ε,η converges uniformly to X in each compact subset of R n \ ∑ when ε, η → 0. We define the sliding region on the non-regular part of Σ as a limit of invariant manifolds of X ε.η . Since the double regularization provides a slow–fast system, the GSP-theory (geometric singular perturbation theory) is our main tool. |
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Repositório Institucional da UNESP |
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2946 |
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Slow–fast systems and sliding on codimension 2 switching manifoldsBogdanov–Takens bifurcationHopf bifurcationinvariant manifoldsnon-smooth systemsSingular perturbationIn this work, we consider piecewise smooth vector fields X defined in R n \ ∑, where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields X ε.η , ε,η > 0 satisfying that X ε,η converges uniformly to X in each compact subset of R n \ ∑ when ε, η → 0. We define the sliding region on the non-regular part of Σ as a limit of invariant manifolds of X ε.η . Since the double regularization provides a slow–fast system, the GSP-theory (geometric singular perturbation theory) is our main tool.Departamento de Matemática–IBILCE–UNESPDepartamento de Matemática–IBILCE–UNESPUniversidade Estadual Paulista (Unesp)da Silva, Paulo Ricardo [UNESP]Nunes, Willian Pereira [UNESP]2019-10-06T16:19:45Z2019-10-06T16:19:45Z2019-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1080/14689367.2019.1579782Dynamical Systems.1468-93751468-9367http://hdl.handle.net/11449/18880510.1080/14689367.2019.15797822-s2.0-8506246344460509558611681610000-0002-1430-5986Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengDynamical Systemsinfo:eu-repo/semantics/openAccess2021-10-23T12:24:07Zoai:repositorio.unesp.br:11449/188805Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:49:26.855002Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Slow–fast systems and sliding on codimension 2 switching manifolds |
title |
Slow–fast systems and sliding on codimension 2 switching manifolds |
spellingShingle |
Slow–fast systems and sliding on codimension 2 switching manifolds da Silva, Paulo Ricardo [UNESP] Bogdanov–Takens bifurcation Hopf bifurcation invariant manifolds non-smooth systems Singular perturbation |
title_short |
Slow–fast systems and sliding on codimension 2 switching manifolds |
title_full |
Slow–fast systems and sliding on codimension 2 switching manifolds |
title_fullStr |
Slow–fast systems and sliding on codimension 2 switching manifolds |
title_full_unstemmed |
Slow–fast systems and sliding on codimension 2 switching manifolds |
title_sort |
Slow–fast systems and sliding on codimension 2 switching manifolds |
author |
da Silva, Paulo Ricardo [UNESP] |
author_facet |
da Silva, Paulo Ricardo [UNESP] Nunes, Willian Pereira [UNESP] |
author_role |
author |
author2 |
Nunes, Willian Pereira [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
da Silva, Paulo Ricardo [UNESP] Nunes, Willian Pereira [UNESP] |
dc.subject.por.fl_str_mv |
Bogdanov–Takens bifurcation Hopf bifurcation invariant manifolds non-smooth systems Singular perturbation |
topic |
Bogdanov–Takens bifurcation Hopf bifurcation invariant manifolds non-smooth systems Singular perturbation |
description |
In this work, we consider piecewise smooth vector fields X defined in R n \ ∑, where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields X ε.η , ε,η > 0 satisfying that X ε,η converges uniformly to X in each compact subset of R n \ ∑ when ε, η → 0. We define the sliding region on the non-regular part of Σ as a limit of invariant manifolds of X ε.η . Since the double regularization provides a slow–fast system, the GSP-theory (geometric singular perturbation theory) is our main tool. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10-06T16:19:45Z 2019-10-06T16:19:45Z 2019-01-01 |
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/10.1080/14689367.2019.1579782 Dynamical Systems. 1468-9375 1468-9367 http://hdl.handle.net/11449/188805 10.1080/14689367.2019.1579782 2-s2.0-85062463444 6050955861168161 0000-0002-1430-5986 |
url |
http://dx.doi.org/10.1080/14689367.2019.1579782 http://hdl.handle.net/11449/188805 |
identifier_str_mv |
Dynamical Systems. 1468-9375 1468-9367 10.1080/14689367.2019.1579782 2-s2.0-85062463444 6050955861168161 0000-0002-1430-5986 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Dynamical Systems |
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 |
|
_version_ |
1808129465727844352 |