Geometry and Global Stability of 2D Periodic Monotone Maps

Detalhes bibliográficos
Autor(a) principal: Balreira, E. Cabral
Data de Publicação: 2021
Outros Autores: 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/10400.13/5438
Resumo: We establish conditions to ensure global stability of a competitive periodic system from hypotheses on individual maps. We study planar competitive maps of Kolgomorov type. We show how conditions for global stability for individual maps will remain invariant under composition and hence establish a globally stable cycle. Our main theoretical contribution is to show that stability for monotone non-autonomous periodic maps can be reduced to a problem of global injectivity. We provide analytic conditions that can be checked and illustrate our results with important competition models such as the planar Leslie-Gower and Ricker maps.
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spelling Geometry and Global Stability of 2D Periodic Monotone MapsCompetition modelsGlobal stabilityKolmogorov mapsMonotone maps2D Periodic maps.Faculdade de Ciências Exatas e da EngenhariaWe establish conditions to ensure global stability of a competitive periodic system from hypotheses on individual maps. We study planar competitive maps of Kolgomorov type. We show how conditions for global stability for individual maps will remain invariant under composition and hence establish a globally stable cycle. Our main theoretical contribution is to show that stability for monotone non-autonomous periodic maps can be reduced to a problem of global injectivity. We provide analytic conditions that can be checked and illustrate our results with important competition models such as the planar Leslie-Gower and Ricker maps.SpringerDigitUMaBalreira, E. CabralLuís, Rafael2023-12-19T13:35:12Z20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.13/5438engBalreira, E. C., & Luís, R. (2021). Geometry and Global Stability of 2D Periodic Monotone Maps. Journal of Dynamics and Differential Equations, 1-14.10.1007/s10884-021-10089-zinfo: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:RCAAP2023-12-24T03:32:04Zoai:digituma.uma.pt:10400.13/5438Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:55:57.023355Repositório 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 Geometry and Global Stability of 2D Periodic Monotone Maps
title Geometry and Global Stability of 2D Periodic Monotone Maps
spellingShingle Geometry and Global Stability of 2D Periodic Monotone Maps
Balreira, E. Cabral
Competition models
Global stability
Kolmogorov maps
Monotone maps
2D Periodic maps
.
Faculdade de Ciências Exatas e da Engenharia
title_short Geometry and Global Stability of 2D Periodic Monotone Maps
title_full Geometry and Global Stability of 2D Periodic Monotone Maps
title_fullStr Geometry and Global Stability of 2D Periodic Monotone Maps
title_full_unstemmed Geometry and Global Stability of 2D Periodic Monotone Maps
title_sort Geometry and Global Stability of 2D Periodic Monotone Maps
author Balreira, E. Cabral
author_facet Balreira, E. Cabral
Luís, Rafael
author_role author
author2 Luís, Rafael
author2_role author
dc.contributor.none.fl_str_mv DigitUMa
dc.contributor.author.fl_str_mv Balreira, E. Cabral
Luís, Rafael
dc.subject.por.fl_str_mv Competition models
Global stability
Kolmogorov maps
Monotone maps
2D Periodic maps
.
Faculdade de Ciências Exatas e da Engenharia
topic Competition models
Global stability
Kolmogorov maps
Monotone maps
2D Periodic maps
.
Faculdade de Ciências Exatas e da Engenharia
description We establish conditions to ensure global stability of a competitive periodic system from hypotheses on individual maps. We study planar competitive maps of Kolgomorov type. We show how conditions for global stability for individual maps will remain invariant under composition and hence establish a globally stable cycle. Our main theoretical contribution is to show that stability for monotone non-autonomous periodic maps can be reduced to a problem of global injectivity. We provide analytic conditions that can be checked and illustrate our results with important competition models such as the planar Leslie-Gower and Ricker maps.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
2023-12-19T13:35:12Z
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/10400.13/5438
url http://hdl.handle.net/10400.13/5438
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Balreira, E. C., & Luís, R. (2021). Geometry and Global Stability of 2D Periodic Monotone Maps. Journal of Dynamics and Differential Equations, 1-14.
10.1007/s10884-021-10089-z
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 Springer
publisher.none.fl_str_mv Springer
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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