Global dynamics of triangular maps

Detalhes bibliográficos
Autor(a) principal: Balreira, E. Cabral
Data de Publicação: 2014
Outros Autores: Elaydi, Saber, Luís, Rafael
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.13/3766
Resumo: We consider continuous triangular maps on I N , where I is a compact interval in the Euclidean space R. We show, under some conditions, that the orbit of every point in a triangular map converges to a fixed point if and only if there is no periodic orbit of prime period two. As a consequence we obtain a result on global stability, namely, if there are no periodic orbits of prime period 2 and the triangular map has a unique fixed point, then the fixed point is globally asymptotically stable. We also discuss examples and applications of our results to competition models.
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spelling Global dynamics of triangular mapsTriangular mapsSharkovsky’s theoremOmega limit setOrbitFiberGlobal stability.Faculdade de Ciências Exatas e da EngenhariaWe consider continuous triangular maps on I N , where I is a compact interval in the Euclidean space R. We show, under some conditions, that the orbit of every point in a triangular map converges to a fixed point if and only if there is no periodic orbit of prime period two. As a consequence we obtain a result on global stability, namely, if there are no periodic orbits of prime period 2 and the triangular map has a unique fixed point, then the fixed point is globally asymptotically stable. We also discuss examples and applications of our results to competition models.ElsevierDigitUMaBalreira, E. CabralElaydi, SaberLuís, Rafael2021-10-26T10:41:13Z20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.13/3766engBalreira, E. C., Elaydi, S., & Luís, R. (2014). Global dynamics of triangular maps. Nonlinear Analysis: Theory, Methods & Applications, 104, 75-83. https://doi.org/10.1016/j.na.2014.03.01910.1016/j.na.2014.03.019info: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:RCAAP2023-12-24T03:31:31Zoai:digituma.uma.pt:10400.13/3766Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T15:07:09.724495Repositório 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 Global dynamics of triangular maps
title Global dynamics of triangular maps
spellingShingle Global dynamics of triangular maps
Balreira, E. Cabral
Triangular maps
Sharkovsky’s theorem
Omega limit set
Orbit
Fiber
Global stability
.
Faculdade de Ciências Exatas e da Engenharia
title_short Global dynamics of triangular maps
title_full Global dynamics of triangular maps
title_fullStr Global dynamics of triangular maps
title_full_unstemmed Global dynamics of triangular maps
title_sort Global dynamics of triangular maps
author Balreira, E. Cabral
author_facet Balreira, E. Cabral
Elaydi, Saber
Luís, Rafael
author_role author
author2 Elaydi, Saber
Luís, Rafael
author2_role author
author
dc.contributor.none.fl_str_mv DigitUMa
dc.contributor.author.fl_str_mv Balreira, E. Cabral
Elaydi, Saber
Luís, Rafael
dc.subject.por.fl_str_mv Triangular maps
Sharkovsky’s theorem
Omega limit set
Orbit
Fiber
Global stability
.
Faculdade de Ciências Exatas e da Engenharia
topic Triangular maps
Sharkovsky’s theorem
Omega limit set
Orbit
Fiber
Global stability
.
Faculdade de Ciências Exatas e da Engenharia
description We consider continuous triangular maps on I N , where I is a compact interval in the Euclidean space R. We show, under some conditions, that the orbit of every point in a triangular map converges to a fixed point if and only if there is no periodic orbit of prime period two. As a consequence we obtain a result on global stability, namely, if there are no periodic orbits of prime period 2 and the triangular map has a unique fixed point, then the fixed point is globally asymptotically stable. We also discuss examples and applications of our results to competition models.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01T00:00:00Z
2021-10-26T10:41:13Z
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/10400.13/3766
url http://hdl.handle.net/10400.13/3766
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Balreira, E. C., Elaydi, S., & Luís, R. (2014). Global dynamics of triangular maps. Nonlinear Analysis: Theory, Methods & Applications, 104, 75-83. https://doi.org/10.1016/j.na.2014.03.019
10.1016/j.na.2014.03.019
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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