Dynamics of a differential system using invariant regions
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/1533 |
Resumo: | The longtime behaviour of a two dimensional system of ordinary differential equations with singularities is studied using conveniently defined positively invariant sets and auxiliary functions. The approach uses only elementary techniques of phase plane analysis and provides a good geometric insight into the dynamical behaviour of the system. It provides dynamical information analogous to what is usually obtained via centre manifold techniques but does not require the flow to be defined at the limit point. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Dynamics of a differential system using invariant regionsOrdinary diferential equationsAsymptotic behaviour of solutionsInvariant regionsThe longtime behaviour of a two dimensional system of ordinary differential equations with singularities is studied using conveniently defined positively invariant sets and auxiliary functions. The approach uses only elementary techniques of phase plane analysis and provides a good geometric insight into the dynamical behaviour of the system. It provides dynamical information analogous to what is usually obtained via centre manifold techniques but does not require the flow to be defined at the limit point.Partially supported by Fundação para a Ciência e a TecnologiaThe International Commission on Mathematical InstructionRepositório AbertoCosta, Fernando Pestana da2010-07-15T13:08:36Z20072007-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/1533engCosta, Fernando Pestana da - Dynamics of a differential system using invariant regions. "L'Enseignement Mathematique" [Em linha]. ISSN 0425-0818. Vol. 53, nº 2 (2007), p. 3-140425-0818info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:14:14Zoai:repositorioaberto.uab.pt:10400.2/1533Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:43:20.926693Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Dynamics of a differential system using invariant regions |
title |
Dynamics of a differential system using invariant regions |
spellingShingle |
Dynamics of a differential system using invariant regions Costa, Fernando Pestana da Ordinary diferential equations Asymptotic behaviour of solutions Invariant regions |
title_short |
Dynamics of a differential system using invariant regions |
title_full |
Dynamics of a differential system using invariant regions |
title_fullStr |
Dynamics of a differential system using invariant regions |
title_full_unstemmed |
Dynamics of a differential system using invariant regions |
title_sort |
Dynamics of a differential system using invariant regions |
author |
Costa, Fernando Pestana da |
author_facet |
Costa, Fernando Pestana da |
author_role |
author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Costa, Fernando Pestana da |
dc.subject.por.fl_str_mv |
Ordinary diferential equations Asymptotic behaviour of solutions Invariant regions |
topic |
Ordinary diferential equations Asymptotic behaviour of solutions Invariant regions |
description |
The longtime behaviour of a two dimensional system of ordinary differential equations with singularities is studied using conveniently defined positively invariant sets and auxiliary functions. The approach uses only elementary techniques of phase plane analysis and provides a good geometric insight into the dynamical behaviour of the system. It provides dynamical information analogous to what is usually obtained via centre manifold techniques but does not require the flow to be defined at the limit point. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007 2007-01-01T00:00:00Z 2010-07-15T13:08:36Z |
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://hdl.handle.net/10400.2/1533 |
url |
http://hdl.handle.net/10400.2/1533 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Costa, Fernando Pestana da - Dynamics of a differential system using invariant regions. "L'Enseignement Mathematique" [Em linha]. ISSN 0425-0818. Vol. 53, nº 2 (2007), p. 3-14 0425-0818 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
The International Commission on Mathematical Instruction |
publisher.none.fl_str_mv |
The International Commission on Mathematical Instruction |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799134999875682304 |