Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points

Detalhes bibliográficos
Autor(a) principal: Amaral,F.M.
Data de Publicação: 2012
Outros Autores: 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=S2179-84512012000200005
Resumo: A dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.
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spelling Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium pointsStability RegionStability BoundarySaddle-Node Equilibrium PointA dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.Sociedade Brasileira de Matemática Aplicada e Computacional2012-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512012000200005TEMA (São Carlos) v.13 n.2 2012reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2012.013.02.0143info:eu-repo/semantics/openAccessAmaral,F.M.Alberto,L.F.C.eng2012-10-15T00:00:00Zoai:scielo:S2179-84512012000200005Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2012-10-15T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points
title Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points
spellingShingle Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points
Amaral,F.M.
Stability Region
Stability Boundary
Saddle-Node Equilibrium Point
title_short Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points
title_full Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points
title_fullStr Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points
title_full_unstemmed Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points
title_sort Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points
author Amaral,F.M.
author_facet Amaral,F.M.
Alberto,L.F.C.
author_role author
author2 Alberto,L.F.C.
author2_role author
dc.contributor.author.fl_str_mv Amaral,F.M.
Alberto,L.F.C.
dc.subject.por.fl_str_mv Stability Region
Stability Boundary
Saddle-Node Equilibrium Point
topic Stability Region
Stability Boundary
Saddle-Node Equilibrium Point
description A dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.
publishDate 2012
dc.date.none.fl_str_mv 2012-01-01
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=S2179-84512012000200005
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512012000200005
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2012.013.02.0143
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.13 n.2 2012
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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