Bifurcation analysis of the γ-Ricker population model using the Lambert W function
Autor(a) principal: | |
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Data de Publicação: | 2020 |
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/10400.21/13388 |
Resumo: | In this work, we present the dynamical study and the bifurcation structures of the γ-Ricker population model. Resorting to the Lambert W function, the analytical solutions of the positive fixed point equation for the γ-Ricker population model are explicitly presented and conditions for the existence and stability of these fixed points are established. The main focus of this work is the definition and characterization of the Allee effect bifurcation for the γ-Ricker population model, which is not a pitchfork bifurcation. Consequently, we prove that the phenomenon of Allee effect for the γ-Ricker population model is associated with the asymptotic behavior of the Lambert W function in a neighborhood of zero. The theoretical results describe the global and local bifurcations of the γ-Ricker population model, using the Lambert W function in the presence and absence of the Allee effect. The Allee effect, snapback repeller and big bang bifurcations are investigated in the parameters space considered. Numerical studies are included. |
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Bifurcation analysis of the γ-Ricker population model using the Lambert W functionγ-Ricker population modelLambert W functionAllee effect bifurcationFold and flip bifurcationsSnapback repeller bifurcationBig bang bifurcationIn this work, we present the dynamical study and the bifurcation structures of the γ-Ricker population model. Resorting to the Lambert W function, the analytical solutions of the positive fixed point equation for the γ-Ricker population model are explicitly presented and conditions for the existence and stability of these fixed points are established. The main focus of this work is the definition and characterization of the Allee effect bifurcation for the γ-Ricker population model, which is not a pitchfork bifurcation. Consequently, we prove that the phenomenon of Allee effect for the γ-Ricker population model is associated with the asymptotic behavior of the Lambert W function in a neighborhood of zero. The theoretical results describe the global and local bifurcations of the γ-Ricker population model, using the Lambert W function in the presence and absence of the Allee effect. The Allee effect, snapback repeller and big bang bifurcations are investigated in the parameters space considered. Numerical studies are included.World Scientific Publishing CompanyRCIPLRocha, J. LeonelTAHA, Abdel-Kaddous2021-05-27T13:43:45Z2020-06-152020-06-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/13388engROCHA, J. Leonel; TAHA, Abdel-Kaddous – Bifurcation analysis of the γ-Ricker population model using the Lambert W function. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. ISSN 0218-1274. Vol. 30, N.º 7 (2020), pp. 2050108-1- 2050108-160218-127410.1142/S02181274205010841793-6551metadata 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:RCAAP2023-08-03T10:08:00Zoai:repositorio.ipl.pt:10400.21/13388Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:21:20.708726Repositório 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 analysis of the γ-Ricker population model using the Lambert W function |
title |
Bifurcation analysis of the γ-Ricker population model using the Lambert W function |
spellingShingle |
Bifurcation analysis of the γ-Ricker population model using the Lambert W function Rocha, J. Leonel γ-Ricker population model Lambert W function Allee effect bifurcation Fold and flip bifurcations Snapback repeller bifurcation Big bang bifurcation |
title_short |
Bifurcation analysis of the γ-Ricker population model using the Lambert W function |
title_full |
Bifurcation analysis of the γ-Ricker population model using the Lambert W function |
title_fullStr |
Bifurcation analysis of the γ-Ricker population model using the Lambert W function |
title_full_unstemmed |
Bifurcation analysis of the γ-Ricker population model using the Lambert W function |
title_sort |
Bifurcation analysis of the γ-Ricker population model using the Lambert W function |
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 |
γ-Ricker population model Lambert W function Allee effect bifurcation Fold and flip bifurcations Snapback repeller bifurcation Big bang bifurcation |
topic |
γ-Ricker population model Lambert W function Allee effect bifurcation Fold and flip bifurcations Snapback repeller bifurcation Big bang bifurcation |
description |
In this work, we present the dynamical study and the bifurcation structures of the γ-Ricker population model. Resorting to the Lambert W function, the analytical solutions of the positive fixed point equation for the γ-Ricker population model are explicitly presented and conditions for the existence and stability of these fixed points are established. The main focus of this work is the definition and characterization of the Allee effect bifurcation for the γ-Ricker population model, which is not a pitchfork bifurcation. Consequently, we prove that the phenomenon of Allee effect for the γ-Ricker population model is associated with the asymptotic behavior of the Lambert W function in a neighborhood of zero. The theoretical results describe the global and local bifurcations of the γ-Ricker population model, using the Lambert W function in the presence and absence of the Allee effect. The Allee effect, snapback repeller and big bang bifurcations are investigated in the parameters space considered. Numerical studies are included. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-06-15 2020-06-15T00:00:00Z 2021-05-27T13:43:45Z |
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/10400.21/13388 |
url |
http://hdl.handle.net/10400.21/13388 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
ROCHA, J. Leonel; TAHA, Abdel-Kaddous – Bifurcation analysis of the γ-Ricker population model using the Lambert W function. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. ISSN 0218-1274. Vol. 30, N.º 7 (2020), pp. 2050108-1- 2050108-16 0218-1274 10.1142/S0218127420501084 1793-6551 |
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 |
World Scientific Publishing Company |
publisher.none.fl_str_mv |
World Scientific Publishing Company |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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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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1799133484039536640 |