Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density

Assuming that the prey refuge is proportional to the prey density if its population size is below a critical threshold, or constant if its size is above the threshold, this paper proposes, and qualitatively analyzes, a Leslie–Gower predator–prey model assuming alternative feeding and harvesting in p...

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Detalles Bibliográficos
Autor: Cortés García, Christian
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/362822
Acceso en línea:http://hdl.handle.net/10261/362822
https://api.elsevier.com/content/abstract/scopus_id/85148694885
Access Level:acceso abierto
Palabra clave:Critical threshold
Crossing region
Filippov systems
Harvesting
Logistic growth
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spelling Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low densityCortés García, ChristianCritical thresholdCrossing regionFilippov systemsHarvestingLogistic growthAssuming that the prey refuge is proportional to the prey density if its population size is below a critical threshold, or constant if its size is above the threshold, this paper proposes, and qualitatively analyzes, a Leslie–Gower predator–prey model assuming alternative feeding and harvesting in predators, and a Holling II function as the predator functional response. From the results of the mathematical analysis to the predator–prey models with proportional or constant prey refuge, the proposed model retains the same bifurcation cases obtained for each model analyzed. However, appropriate alterations of the parameters representing the critical threshold of prey population size and harvest in predators allows the formation of at least one limit cycle, stable or unstable, that lives in both vector fields of the proposed model.This research was supported by MCIN/AEI/10.13039/501100011033 through grant BADS, no. PID2019- 109320GB-100, and the associated FPI contract PRE2019-088899 to Christian Cort ́es Garc ́ıa. The Spanish MICINN has also funded the “Severo Ochoa” Centers of Excellence to CNB, SEV 2017-0712.Peer reviewedElsevierMinisterio de Ciencia e Innovación (España)Ministerio de Ciencia, Innovación y Universidades (España)Cortés García, Christian [0000-0002-8955-4530]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202420242023info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/362822https://api.elsevier.com/content/abstract/scopus_id/85148694885reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-109320GB-I00info:eu-repo/grantAgreement/AEI/Plan Estatal de investigación Científica y Técnica y de Innovación/SEV 2017-0712Nonlinear Analysis: Real World Applicationsapplication/pdfhttps://www.sciencedirect.com/science/article/pii/S1468121823000317?via%3DihubSíinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3628222026-05-22T06:33:51Z
dc.title.none.fl_str_mv Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density
title Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density
spellingShingle Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density
Cortés García, Christian
Critical threshold
Crossing region
Filippov systems
Harvesting
Logistic growth
title_short Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density
title_full Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density
title_fullStr Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density
title_full_unstemmed Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density
title_sort Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density
dc.creator.none.fl_str_mv Cortés García, Christian
author Cortés García, Christian
author_facet Cortés García, Christian
author_role author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
Ministerio de Ciencia, Innovación y Universidades (España)
Cortés García, Christian [0000-0002-8955-4530]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Critical threshold
Crossing region
Filippov systems
Harvesting
Logistic growth
topic Critical threshold
Crossing region
Filippov systems
Harvesting
Logistic growth
description Assuming that the prey refuge is proportional to the prey density if its population size is below a critical threshold, or constant if its size is above the threshold, this paper proposes, and qualitatively analyzes, a Leslie–Gower predator–prey model assuming alternative feeding and harvesting in predators, and a Holling II function as the predator functional response. From the results of the mathematical analysis to the predator–prey models with proportional or constant prey refuge, the proposed model retains the same bifurcation cases obtained for each model analyzed. However, appropriate alterations of the parameters representing the critical threshold of prey population size and harvest in predators allows the formation of at least one limit cycle, stable or unstable, that lives in both vector fields of the proposed model.
publishDate 2023
dc.date.none.fl_str_mv 2023
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/362822
https://api.elsevier.com/content/abstract/scopus_id/85148694885
url http://hdl.handle.net/10261/362822
https://api.elsevier.com/content/abstract/scopus_id/85148694885
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
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info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-109320GB-I00
info:eu-repo/grantAgreement/AEI/Plan Estatal de investigación Científica y Técnica y de Innovación/SEV 2017-0712
Nonlinear Analysis: Real World Applications
application/pdf
https://www.sciencedirect.com/science/article/pii/S1468121823000317?via%3Dihub
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
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