On chaos, transient chaos and ghosts in single populations models with allee effects
Autor(a) principal: | |
---|---|
Data de Publicação: | 2012 |
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/10400.21/5135 |
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. |
id |
RCAP_5ac53da1fd7117e10f85b70ad24ab9d6 |
---|---|
oai_identifier_str |
oai:repositorio.ipl.pt:10400.21/5135 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
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 |
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 application/pdf |
dc.publisher.none.fl_str_mv |
Pergamon-Elsevier |
publisher.none.fl_str_mv |
Pergamon-Elsevier |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799133402441449472 |