Computability in planar dynamical systems

Detalhes bibliográficos
Autor(a) principal: Graça, Daniel
Data de Publicação: 2011
Outros Autores: Zhong, Ning
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/1005
Resumo: In this paper we explore the problem of computing attractors and their respective basins of attraction for continuous-time planar dynamical systems. We consider C1 systems and show that stability is in general necessary (but may not be sufficient) to attain computability. In particular, we show that (a) the problem of determining the number of attractors in a given compact set is in general undecidable, even for analytic systems and (b) the attractors are semi-computable for stable systems. We also show that the basins of attraction are semi-computable if and only if the system is stable.
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spelling Computability in planar dynamical systemsComputabilityEquilibrium pointsPlanar dynamical systemsIn this paper we explore the problem of computing attractors and their respective basins of attraction for continuous-time planar dynamical systems. We consider C1 systems and show that stability is in general necessary (but may not be sufficient) to attain computability. In particular, we show that (a) the problem of determining the number of attractors in a given compact set is in general undecidable, even for analytic systems and (b) the attractors are semi-computable for stable systems. We also show that the basins of attraction are semi-computable if and only if the system is stable.SapientiaGraça, DanielZhong, Ning2012-04-13T08:03:35Z20112011-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/1005engAUT: DGR01772;info: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:RCAAP2023-07-24T10:11:57Zoai:sapientia.ualg.pt:10400.1/1005Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:55:17.015039Repositório 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 Computability in planar dynamical systems
title Computability in planar dynamical systems
spellingShingle Computability in planar dynamical systems
Graça, Daniel
Computability
Equilibrium points
Planar dynamical systems
title_short Computability in planar dynamical systems
title_full Computability in planar dynamical systems
title_fullStr Computability in planar dynamical systems
title_full_unstemmed Computability in planar dynamical systems
title_sort Computability in planar dynamical systems
author Graça, Daniel
author_facet Graça, Daniel
Zhong, Ning
author_role author
author2 Zhong, Ning
author2_role author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Graça, Daniel
Zhong, Ning
dc.subject.por.fl_str_mv Computability
Equilibrium points
Planar dynamical systems
topic Computability
Equilibrium points
Planar dynamical systems
description In this paper we explore the problem of computing attractors and their respective basins of attraction for continuous-time planar dynamical systems. We consider C1 systems and show that stability is in general necessary (but may not be sufficient) to attain computability. In particular, we show that (a) the problem of determining the number of attractors in a given compact set is in general undecidable, even for analytic systems and (b) the attractors are semi-computable for stable systems. We also show that the basins of attraction are semi-computable if and only if the system is stable.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-01-01T00:00:00Z
2012-04-13T08:03:35Z
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/10400.1/1005
url http://hdl.handle.net/10400.1/1005
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv AUT: DGR01772;
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.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
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