Bifurcation structures in a 2D exponential diffeomorphism with Allee effect

Detalhes bibliográficos
Autor(a) principal: Rocha, J. Leonel
Data de Publicação: 2019
Outros Autores: Taha, Abdel-Kaddous
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/9319
Resumo: An embedding of one-dimensional generic growth functions into a two-dimensional diffeomorphism is considered. This family of unimodal maps naturally incorporates a key item of ecological and biological research: the Allee effect. Consequently, the presence of this species extinction phenomenon leads us to a new definition of bifurcation for this two-dimensional exponential diffeomorphism: Allee’s effect bifurcation. The stability and the nature of the fixed points of the two-dimensional diffeomorphism are analyzed, by studying the corresponding contour lines. Fold and flip bifurcation structures of this exponential diffeomorphism are investigated, in which there are flip codimension-2 bifurcation points and cusp points, when some parameters evolve. Numerical studies are included.
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spelling Bifurcation structures in a 2D exponential diffeomorphism with Allee effectAllee’s effect bifurcationFold and flip bifurcationsDiffeomorphismsContour lineLinha de contornoDobrar e virar bifurcaçõesAn embedding of one-dimensional generic growth functions into a two-dimensional diffeomorphism is considered. This family of unimodal maps naturally incorporates a key item of ecological and biological research: the Allee effect. Consequently, the presence of this species extinction phenomenon leads us to a new definition of bifurcation for this two-dimensional exponential diffeomorphism: Allee’s effect bifurcation. The stability and the nature of the fixed points of the two-dimensional diffeomorphism are analyzed, by studying the corresponding contour lines. Fold and flip bifurcation structures of this exponential diffeomorphism are investigated, in which there are flip codimension-2 bifurcation points and cusp points, when some parameters evolve. Numerical studies are included.SpringerRCIPLRocha, J. LeonelTaha, Abdel-Kaddous2019-01-14T10:26:15Z2019-032019-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/9319engROCHA, J. Leonel; TAHA, Abdel-Kaddous – Bifurcation structures in a 2D exponential diffeomorphism with Allee effect. Nonlinear Dynamics. ISSN 0924-090X. Vol. 95, N.º 4 (2019), pp. 3357-33740924-090Xhttps://doi.org/10.1007/s11071-019-04759-3metadata only accessinfo: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:RCAAP2023-08-03T09:57:51Zoai:repositorio.ipl.pt:10400.21/9319Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:17:54.893425Repositório 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 Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
title Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
spellingShingle Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
Rocha, J. Leonel
Allee’s effect bifurcation
Fold and flip bifurcations
Diffeomorphisms
Contour line
Linha de contorno
Dobrar e virar bifurcações
title_short Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
title_full Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
title_fullStr Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
title_full_unstemmed Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
title_sort Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
author Rocha, J. Leonel
author_facet Rocha, J. Leonel
Taha, Abdel-Kaddous
author_role author
author2 Taha, Abdel-Kaddous
author2_role author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Rocha, J. Leonel
Taha, Abdel-Kaddous
dc.subject.por.fl_str_mv Allee’s effect bifurcation
Fold and flip bifurcations
Diffeomorphisms
Contour line
Linha de contorno
Dobrar e virar bifurcações
topic Allee’s effect bifurcation
Fold and flip bifurcations
Diffeomorphisms
Contour line
Linha de contorno
Dobrar e virar bifurcações
description An embedding of one-dimensional generic growth functions into a two-dimensional diffeomorphism is considered. This family of unimodal maps naturally incorporates a key item of ecological and biological research: the Allee effect. Consequently, the presence of this species extinction phenomenon leads us to a new definition of bifurcation for this two-dimensional exponential diffeomorphism: Allee’s effect bifurcation. The stability and the nature of the fixed points of the two-dimensional diffeomorphism are analyzed, by studying the corresponding contour lines. Fold and flip bifurcation structures of this exponential diffeomorphism are investigated, in which there are flip codimension-2 bifurcation points and cusp points, when some parameters evolve. Numerical studies are included.
publishDate 2019
dc.date.none.fl_str_mv 2019-01-14T10:26:15Z
2019-03
2019-03-01T00:00:00Z
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/10400.21/9319
url http://hdl.handle.net/10400.21/9319
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv ROCHA, J. Leonel; TAHA, Abdel-Kaddous – Bifurcation structures in a 2D exponential diffeomorphism with Allee effect. Nonlinear Dynamics. ISSN 0924-090X. Vol. 95, N.º 4 (2019), pp. 3357-3374
0924-090X
https://doi.org/10.1007/s11071-019-04759-3
dc.rights.driver.fl_str_mv metadata only access
info:eu-repo/semantics/openAccess
rights_invalid_str_mv metadata only access
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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