Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response

Since certain prey hide from predators to protect themselves within their habitats, predators are forced to change their diet due to a lack of prey for consumption, or on the contrary, subsist only with alternative food provided by the environment. Therefore, in this paper, we propose and mathematic...

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Detalhes bibliográficos
Autores: García, Christian Cortés, Cuenca, Jasmidt Vera
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/363462
Acesso em linha:http://hdl.handle.net/10261/363462
https://api.elsevier.com/content/abstract/scopus_id/85164768198
Access Level:acceso abierto
Palavra-chave:bifurcation theory
critical threshold
crossing region
filippov systems
harvesting
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spelling Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional responseGarcía, Christian CortésCuenca, Jasmidt Verabifurcation theorycritical thresholdcrossing regionfilippov systemsharvestingSince certain prey hide from predators to protect themselves within their habitats, predators are forced to change their diet due to a lack of prey for consumption, or on the contrary, subsist only with alternative food provided by the environment. Therefore, in this paper, we propose and mathematically contrast a predator-prey, where alternative food for predators is either considered or not when the prey population size is above the refuge threshold size. Since the model with no alternative food for predators has a Hopf bifurcation and a transcritical bifurcation, in addition to a stable limit cycle surrounding the unique interior equilibrium, such bifurcation cases are transferred to the model when considering alternative food for predators when the prey size is above the refuge. However, such a model has two saddle-node bifurcations and a homoclinic bifurcation, characterized by a homoclinic curve surrounding one of the three interior equilibrium points of the 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 Corte ́s Garc ́ıa. The Spanish MICINN has also funded the “Severo Ochoa” Centers of Excellence to CNB, SEV 2017-0712.Peer reviewedAIMS PressMinisterio de Ciencia e Innovación (España)García, Christian Cortés [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/10261/363462https://api.elsevier.com/content/abstract/scopus_id/85164768198reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-109320GB-I00Mathematical biosciences and engineering : MBEapplication/pdfhttp://www.aimspress.com/article/doi/10.3934/mbe.2023610Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3634622026-05-22T06:33:51Z
dc.title.none.fl_str_mv Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response
title Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response
spellingShingle Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response
García, Christian Cortés
bifurcation theory
critical threshold
crossing region
filippov systems
harvesting
title_short Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response
title_full Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response
title_fullStr Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response
title_full_unstemmed Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response
title_sort Impact of alternative food on predator diet in a Leslie-Gower model with prey refuge and Holling Ⅱ functional response
dc.creator.none.fl_str_mv García, Christian Cortés
Cuenca, Jasmidt Vera
author García, Christian Cortés
author_facet García, Christian Cortés
Cuenca, Jasmidt Vera
author_role author
author2 Cuenca, Jasmidt Vera
author2_role author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
García, Christian Cortés [0000-0002-8955-4530]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv bifurcation theory
critical threshold
crossing region
filippov systems
harvesting
topic bifurcation theory
critical threshold
crossing region
filippov systems
harvesting
description Since certain prey hide from predators to protect themselves within their habitats, predators are forced to change their diet due to a lack of prey for consumption, or on the contrary, subsist only with alternative food provided by the environment. Therefore, in this paper, we propose and mathematically contrast a predator-prey, where alternative food for predators is either considered or not when the prey population size is above the refuge threshold size. Since the model with no alternative food for predators has a Hopf bifurcation and a transcritical bifurcation, in addition to a stable limit cycle surrounding the unique interior equilibrium, such bifurcation cases are transferred to the model when considering alternative food for predators when the prey size is above the refuge. However, such a model has two saddle-node bifurcations and a homoclinic bifurcation, characterized by a homoclinic curve surrounding one of the three interior equilibrium points of the 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/10261/363462
https://api.elsevier.com/content/abstract/scopus_id/85164768198
url http://hdl.handle.net/10261/363462
https://api.elsevier.com/content/abstract/scopus_id/85164768198
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-109320GB-I00
Mathematical biosciences and engineering : MBE
application/pdf
http://www.aimspress.com/article/doi/10.3934/mbe.2023610
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv AIMS Press
publisher.none.fl_str_mv AIMS Press
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)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
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