Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/10400.21/6290 |
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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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 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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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