Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

Detalhes bibliográficos
Autor(a) principal: Rocha, J. Leonel
Data de Publicação: 2016
Outros Autores: Taha, Abdel-Kaddous, Fournier-Prunaret, Danièle
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/6290
Resumo: The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.
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spelling Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effectsVon Bertalanffy's dynamicsStrong and weak Allee effectsBig bang bifurcationExtinctionThe main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.SpringerRCIPLRocha, J. LeonelTaha, Abdel-KaddousFournier-Prunaret, Danièle2016-07-04T11:34:29Z2016-042016-04-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/6290engROCHA, J. Leonel; TAHA, Abdel-Kaddous; FOURNIER-PRUNARET, Danièle - Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects. Nonlinear dynamics. ISSN 0924-090X. Vol. 84, Nr. 2, (2016), 607-626.0924-090X10.1007/s11071-015-2510-6metadata 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:RCAAP2023-08-03T09:50:55Zoai:repositorio.ipl.pt:10400.21/6290Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:15:26.954613Repositório 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 Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
title Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
spellingShingle Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
Rocha, J. Leonel
Von Bertalanffy's dynamics
Strong and weak Allee effects
Big bang bifurcation
Extinction
title_short Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
title_full Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
title_fullStr Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
title_full_unstemmed Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
title_sort Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
author Rocha, J. Leonel
author_facet Rocha, J. Leonel
Taha, Abdel-Kaddous
Fournier-Prunaret, Danièle
author_role author
author2 Taha, Abdel-Kaddous
Fournier-Prunaret, Danièle
author2_role author
author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Rocha, J. Leonel
Taha, Abdel-Kaddous
Fournier-Prunaret, Danièle
dc.subject.por.fl_str_mv Von Bertalanffy's dynamics
Strong and weak Allee effects
Big bang bifurcation
Extinction
topic Von Bertalanffy's dynamics
Strong and weak Allee effects
Big bang bifurcation
Extinction
description The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.
publishDate 2016
dc.date.none.fl_str_mv 2016-07-04T11:34:29Z
2016-04
2016-04-01T00:00:00Z
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/10400.21/6290
url http://hdl.handle.net/10400.21/6290
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv ROCHA, J. Leonel; TAHA, Abdel-Kaddous; FOURNIER-PRUNARET, Danièle - Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects. Nonlinear dynamics. ISSN 0924-090X. Vol. 84, Nr. 2, (2016), 607-626.
0924-090X
10.1007/s11071-015-2510-6
dc.rights.driver.fl_str_mv metadata only access
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dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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