Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects

Detalhes bibliográficos
Autor(a) principal: Rocha, J. Leonel
Data de Publicação: 2016
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/8584
Resumo: The interest and the relevance of the study of population dynamics and extinction phenomenon are the main motivation to investigate the induction of Allee effects in Gompertz’s logistic growth equation. The stability analysis of the equilibrium points of Gompertz’s logistic growth equation under strong, weak and no Allee effects is presented. Properties and sufficient conditions for the existence of strong, weak and no Allee effects for these new continuous population growth models are provided and discussed. It is established a sufficient condition to prove that the time evolution of the population density to the stable equilibria gets larger, as the Allee effects get stronger. These continuous population growth models subjected to Allee effects take longer time to reach its equilibrium states. The developed models are validated using the Icelandic herring population, with GPDD Id.1765.
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spelling Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effectsGompertz logistic growth equationStability analysisStrong Allee effectsWeak Allee effectsThe interest and the relevance of the study of population dynamics and extinction phenomenon are the main motivation to investigate the induction of Allee effects in Gompertz’s logistic growth equation. The stability analysis of the equilibrium points of Gompertz’s logistic growth equation under strong, weak and no Allee effects is presented. Properties and sufficient conditions for the existence of strong, weak and no Allee effects for these new continuous population growth models are provided and discussed. It is established a sufficient condition to prove that the time evolution of the population density to the stable equilibria gets larger, as the Allee effects get stronger. These continuous population growth models subjected to Allee effects take longer time to reach its equilibrium states. The developed models are validated using the Icelandic herring population, with GPDD Id.1765.World Scientific and Engineering Academy and SocietyRCIPLRocha, J. Leonel2018-06-07T09:43:34Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/8584engROCHA, J. Leonel – Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects. WSEAS Transactions on Mathematics. ISSN 1109-2769. Vol. 15, (2016), pp. 578-587.1109-2769metadata 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:RCAAP2023-08-03T09:56:12Zoai:repositorio.ipl.pt:10400.21/8584Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:17:19.373851Repositório 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 Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
title Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
spellingShingle Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
Rocha, J. Leonel
Gompertz logistic growth equation
Stability analysis
Strong Allee effects
Weak Allee effects
title_short Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
title_full Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
title_fullStr Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
title_full_unstemmed Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
title_sort Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
author Rocha, J. Leonel
author_facet Rocha, J. Leonel
author_role author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Rocha, J. Leonel
dc.subject.por.fl_str_mv Gompertz logistic growth equation
Stability analysis
Strong Allee effects
Weak Allee effects
topic Gompertz logistic growth equation
Stability analysis
Strong Allee effects
Weak Allee effects
description The interest and the relevance of the study of population dynamics and extinction phenomenon are the main motivation to investigate the induction of Allee effects in Gompertz’s logistic growth equation. The stability analysis of the equilibrium points of Gompertz’s logistic growth equation under strong, weak and no Allee effects is presented. Properties and sufficient conditions for the existence of strong, weak and no Allee effects for these new continuous population growth models are provided and discussed. It is established a sufficient condition to prove that the time evolution of the population density to the stable equilibria gets larger, as the Allee effects get stronger. These continuous population growth models subjected to Allee effects take longer time to reach its equilibrium states. The developed models are validated using the Icelandic herring population, with GPDD Id.1765.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
2018-06-07T09:43:34Z
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/10400.21/8584
url http://hdl.handle.net/10400.21/8584
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv ROCHA, J. Leonel – Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects. WSEAS Transactions on Mathematics. ISSN 1109-2769. Vol. 15, (2016), pp. 578-587.
1109-2769
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 World Scientific and Engineering Academy and Society
publisher.none.fl_str_mv World Scientific and Engineering Academy and Society
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
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