Global stability of higher dimensional monotone maps
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.13/5435 |
Resumo: | We develop a notion of monotonicity for maps defined on Euclidean spaces Rk +, of arbitrary dimension k. This is a geometric approach that extends the classical notion of planar monotone maps or planar competitive difference equations. For planar maps, we show that our notion and the classical notion of monotonicity are equivalent. In higher dimensions, we establish certain verifiable conditions under which Kolmogorov monotone maps on Rk + have a globally asymptotically stable fixed point. We apply our results to two competition population models, the Leslie–Gower and the Ricker models of two- and three-species. It is shown that these two models have a unique interior fixed point that is globally asymptotically stable. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Global stability of higher dimensional monotone mapsGlobal stabilityMonotone mapsRicker competition modelLeslie–Gower competition modelCompetitive maps.Faculdade de Ciências Exatas e da EngenhariaWe develop a notion of monotonicity for maps defined on Euclidean spaces Rk +, of arbitrary dimension k. This is a geometric approach that extends the classical notion of planar monotone maps or planar competitive difference equations. For planar maps, we show that our notion and the classical notion of monotonicity are equivalent. In higher dimensions, we establish certain verifiable conditions under which Kolmogorov monotone maps on Rk + have a globally asymptotically stable fixed point. We apply our results to two competition population models, the Leslie–Gower and the Ricker models of two- and three-species. It is shown that these two models have a unique interior fixed point that is globally asymptotically stable.Taylor and FrancisDigitUMaBalreira, E. CabralElaydi, SaberLuís, Rafael2023-12-19T11:31:17Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.13/5435eng: E. Cabral Balreira, Saber Elaydi & Rafael Luís (2017) Global stability of higher dimensional monotone maps, Journal of Difference Equations and Applications, 23:12, 2037-2071, DOI: 10.1080/10236198.2017.138837510.1080/10236198.2017.1388375info: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:RCAAP2023-12-24T03:32:01Zoai:digituma.uma.pt:10400.13/5435Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:55:56.874952Repositório 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 stability of higher dimensional monotone maps |
title |
Global stability of higher dimensional monotone maps |
spellingShingle |
Global stability of higher dimensional monotone maps Balreira, E. Cabral Global stability Monotone maps Ricker competition model Leslie–Gower competition model Competitive maps . Faculdade de Ciências Exatas e da Engenharia |
title_short |
Global stability of higher dimensional monotone maps |
title_full |
Global stability of higher dimensional monotone maps |
title_fullStr |
Global stability of higher dimensional monotone maps |
title_full_unstemmed |
Global stability of higher dimensional monotone maps |
title_sort |
Global stability of higher dimensional monotone 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 |
Global stability Monotone maps Ricker competition model Leslie–Gower competition model Competitive maps . Faculdade de Ciências Exatas e da Engenharia |
topic |
Global stability Monotone maps Ricker competition model Leslie–Gower competition model Competitive maps . Faculdade de Ciências Exatas e da Engenharia |
description |
We develop a notion of monotonicity for maps defined on Euclidean spaces Rk +, of arbitrary dimension k. This is a geometric approach that extends the classical notion of planar monotone maps or planar competitive difference equations. For planar maps, we show that our notion and the classical notion of monotonicity are equivalent. In higher dimensions, we establish certain verifiable conditions under which Kolmogorov monotone maps on Rk + have a globally asymptotically stable fixed point. We apply our results to two competition population models, the Leslie–Gower and the Ricker models of two- and three-species. It is shown that these two models have a unique interior fixed point that is globally asymptotically stable. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 2017-01-01T00:00:00Z 2023-12-19T11:31:17Z |
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/10400.13/5435 |
url |
http://hdl.handle.net/10400.13/5435 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
: E. Cabral Balreira, Saber Elaydi & Rafael Luís (2017) Global stability of higher dimensional monotone maps, Journal of Difference Equations and Applications, 23:12, 2037-2071, DOI: 10.1080/10236198.2017.1388375 10.1080/10236198.2017.1388375 |
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 |
Taylor and Francis |
publisher.none.fl_str_mv |
Taylor and Francis |
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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1799136445131128832 |