Big Bang bifurcations and allee effect in Blumberg’s dynamics
Autor(a) principal: | |
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Data de Publicação: | 2014 |
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/10400.21/5001 |
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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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 |
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 |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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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1799133401561694208 |