On chaos, transient chaos and ghosts in single populations models with allee effects

Detalhes bibliográficos
Autor(a) principal: Duarte, Jorge
Data de Publicação: 2012
Outros Autores: Januário, Cristina, Martins, Nuno, Sardanyés, Josep
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/5135
Resumo: Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.
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spelling On chaos, transient chaos and ghosts in single populations models with allee effectsAllee EffectsChaosExtinction TransientsScaling LawsSingle Species DynamicsTheoretical EcologyTopological EntropyDensity-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.Pergamon-ElsevierRCIPLDuarte, JorgeJanuário, CristinaMartins, NunoSardanyés, Josep2015-09-10T09:49:35Z2012-082012-08-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/10400.21/5135engDUARTE, J.; JANUÁRIO, C.; MARTINS, N.; SARDANYES, J. – On chaos, transiente chaos and ghosts in single populations models with allee effects. Nonlinear Analysis-Real World Applications. ISSN: 1468-1218. Vol. 13, nr. 4 (2012), pp. 1674-1661.1468-121810.1016/j.nonrwa.2011.11.022metadata 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:RCAAP2023-08-03T09:48:06Zoai:repositorio.ipl.pt:10400.21/5135Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:14:27.449799Repositório 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 On chaos, transient chaos and ghosts in single populations models with allee effects
title On chaos, transient chaos and ghosts in single populations models with allee effects
spellingShingle On chaos, transient chaos and ghosts in single populations models with allee effects
Duarte, Jorge
Allee Effects
Chaos
Extinction Transients
Scaling Laws
Single Species Dynamics
Theoretical Ecology
Topological Entropy
title_short On chaos, transient chaos and ghosts in single populations models with allee effects
title_full On chaos, transient chaos and ghosts in single populations models with allee effects
title_fullStr On chaos, transient chaos and ghosts in single populations models with allee effects
title_full_unstemmed On chaos, transient chaos and ghosts in single populations models with allee effects
title_sort On chaos, transient chaos and ghosts in single populations models with allee effects
author Duarte, Jorge
author_facet Duarte, Jorge
Januário, Cristina
Martins, Nuno
Sardanyés, Josep
author_role author
author2 Januário, Cristina
Martins, Nuno
Sardanyés, Josep
author2_role author
author
author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Duarte, Jorge
Januário, Cristina
Martins, Nuno
Sardanyés, Josep
dc.subject.por.fl_str_mv Allee Effects
Chaos
Extinction Transients
Scaling Laws
Single Species Dynamics
Theoretical Ecology
Topological Entropy
topic Allee Effects
Chaos
Extinction Transients
Scaling Laws
Single Species Dynamics
Theoretical Ecology
Topological Entropy
description Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.
publishDate 2012
dc.date.none.fl_str_mv 2012-08
2012-08-01T00:00:00Z
2015-09-10T09:49:35Z
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/10400.21/5135
url http://hdl.handle.net/10400.21/5135
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv DUARTE, J.; JANUÁRIO, C.; MARTINS, N.; SARDANYES, J. – On chaos, transiente chaos and ghosts in single populations models with allee effects. Nonlinear Analysis-Real World Applications. ISSN: 1468-1218. Vol. 13, nr. 4 (2012), pp. 1674-1661.
1468-1218
10.1016/j.nonrwa.2011.11.022
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dc.publisher.none.fl_str_mv Pergamon-Elsevier
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dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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