Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects
Autor(a) principal: | |
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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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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 |
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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 |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
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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1799133435196866560 |