Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region

Detalhes bibliográficos
Autor(a) principal: GOUVEIA Jr,J.R.R.
Data de Publicação: 2016
Outros Autores: AMARAL,F.M., ALBERTO,L.F.C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512016000200211
Resumo: ABSTRACT A complete characterization of the boundary of the stability region of a class of nonlinear autonomous dynamical systems is developed admitting the existence of Subcritical Hopf nonhyperbolic equilibrium points on the boundary of the stability region. The characterization of the stability region developed in this paper is an extension of the characterization already developed in the literature, which considers only hyperbolic equilibrium point. Under the transversality condition, it is shown the boundary of the stability region is comprised of the stable manifolds of all equilibrium points on the boundary of the stability region, including the stable manifolds of the subcritical Hopf equilibrium points of type k, with 0 ≤ k ≤ n - 2, which belong to the boundary of the stability region.
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spelling Subcritical Hopf Equilibrium Points in the Boundary of the Stability Regiondynamical systemsnonlinear systemsstability regionboundary of the stability regionsubcritical Hopf equilibrium pointABSTRACT A complete characterization of the boundary of the stability region of a class of nonlinear autonomous dynamical systems is developed admitting the existence of Subcritical Hopf nonhyperbolic equilibrium points on the boundary of the stability region. The characterization of the stability region developed in this paper is an extension of the characterization already developed in the literature, which considers only hyperbolic equilibrium point. Under the transversality condition, it is shown the boundary of the stability region is comprised of the stable manifolds of all equilibrium points on the boundary of the stability region, including the stable manifolds of the subcritical Hopf equilibrium points of type k, with 0 ≤ k ≤ n - 2, which belong to the boundary of the stability region.Sociedade Brasileira de Matemática Aplicada e Computacional2016-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512016000200211TEMA (São Carlos) v.17 n.2 2016reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2016.017.02.0211info:eu-repo/semantics/openAccessGOUVEIA Jr,J.R.R.AMARAL,F.M.ALBERTO,L.F.C.eng2016-10-03T00:00:00Zoai:scielo:S2179-84512016000200211Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2016-10-03T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region
title Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region
spellingShingle Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region
GOUVEIA Jr,J.R.R.
dynamical systems
nonlinear systems
stability region
boundary of the stability region
subcritical Hopf equilibrium point
title_short Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region
title_full Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region
title_fullStr Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region
title_full_unstemmed Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region
title_sort Subcritical Hopf Equilibrium Points in the Boundary of the Stability Region
author GOUVEIA Jr,J.R.R.
author_facet GOUVEIA Jr,J.R.R.
AMARAL,F.M.
ALBERTO,L.F.C.
author_role author
author2 AMARAL,F.M.
ALBERTO,L.F.C.
author2_role author
author
dc.contributor.author.fl_str_mv GOUVEIA Jr,J.R.R.
AMARAL,F.M.
ALBERTO,L.F.C.
dc.subject.por.fl_str_mv dynamical systems
nonlinear systems
stability region
boundary of the stability region
subcritical Hopf equilibrium point
topic dynamical systems
nonlinear systems
stability region
boundary of the stability region
subcritical Hopf equilibrium point
description ABSTRACT A complete characterization of the boundary of the stability region of a class of nonlinear autonomous dynamical systems is developed admitting the existence of Subcritical Hopf nonhyperbolic equilibrium points on the boundary of the stability region. The characterization of the stability region developed in this paper is an extension of the characterization already developed in the literature, which considers only hyperbolic equilibrium point. Under the transversality condition, it is shown the boundary of the stability region is comprised of the stable manifolds of all equilibrium points on the boundary of the stability region, including the stable manifolds of the subcritical Hopf equilibrium points of type k, with 0 ≤ k ≤ n - 2, which belong to the boundary of the stability region.
publishDate 2016
dc.date.none.fl_str_mv 2016-08-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512016000200211
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512016000200211
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2016.017.02.0211
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.17 n.2 2016
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
institution SBMAC
reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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