Big Bang bifurcations and allee effect in Blumberg’s dynamics

Detalhes bibliográficos
Autor(a) principal: Rocha, J. Leonel
Data de Publicação: 2014
Outros Autores: Fournier-Prunaret, Danièle, 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/10400.21/5001
Resumo: This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.
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spelling Big Bang bifurcations and allee effect in Blumberg’s dynamicsBlumberg's DynamicsBig Bang BifurcationsAllee EffectThis paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.SpringerRCIPLRocha, J. LeonelFournier-Prunaret, DanièleTaha, Abdel-Kaddous2015-08-25T13:41:06Z2014-092014-09-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/5001engROCHA, José Leonel Linhares da; FOURNIER-PRUNARET, Daniele; TAHA, Abdel-Kaddous – Big Bang bifurcations and allee effect in Blumberg’s dynamics. Nonlinear Dynamics. ISSN: 0924-090X. Vol. 77, nr. 4 (2014), pp. 1749-17110924-090X10.1007/s11071-014-1415-0metadata 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:RCAAP2023-08-03T09:47:49Zoai:repositorio.ipl.pt:10400.21/5001Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:14:20.987470Repositório 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 and allee effect in Blumberg’s dynamics
title Big Bang bifurcations and allee effect in Blumberg’s dynamics
spellingShingle Big Bang bifurcations and allee effect in Blumberg’s dynamics
Rocha, J. Leonel
Blumberg's Dynamics
Big Bang Bifurcations
Allee Effect
title_short Big Bang bifurcations and allee effect in Blumberg’s dynamics
title_full Big Bang bifurcations and allee effect in Blumberg’s dynamics
title_fullStr Big Bang bifurcations and allee effect in Blumberg’s dynamics
title_full_unstemmed Big Bang bifurcations and allee effect in Blumberg’s dynamics
title_sort Big Bang bifurcations and allee effect in Blumberg’s dynamics
author Rocha, J. Leonel
author_facet Rocha, J. Leonel
Fournier-Prunaret, Danièle
Taha, Abdel-Kaddous
author_role author
author2 Fournier-Prunaret, Danièle
Taha, Abdel-Kaddous
author2_role author
author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Rocha, J. Leonel
Fournier-Prunaret, Danièle
Taha, Abdel-Kaddous
dc.subject.por.fl_str_mv Blumberg's Dynamics
Big Bang Bifurcations
Allee Effect
topic Blumberg's Dynamics
Big Bang Bifurcations
Allee Effect
description This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.
publishDate 2014
dc.date.none.fl_str_mv 2014-09
2014-09-01T00:00:00Z
2015-08-25T13:41:06Z
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/10400.21/5001
url http://hdl.handle.net/10400.21/5001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv ROCHA, José Leonel Linhares da; FOURNIER-PRUNARET, Daniele; TAHA, Abdel-Kaddous – Big Bang bifurcations and allee effect in Blumberg’s dynamics. Nonlinear Dynamics. ISSN: 0924-090X. Vol. 77, nr. 4 (2014), pp. 1749-1711
0924-090X
10.1007/s11071-014-1415-0
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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)
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