Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses

In this paper we analyze the dynamics of a tritrophic food chain, with functional responses of Holling type III and II for the mesopredator and superpredator respectively and logistic growth rate for the prey. We show that there are parameter conditions for which the system has up to three equilibri...

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Detalles Bibliográficos
Autores principales: Blé, Gamaliel, Castellanos, Víctor, Castillo-Santos, Francisco Eduardo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2021
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7902555/
https://www.ncbi.nlm.nih.gov/pubmed/33665414
http://dx.doi.org/10.1016/j.heliyon.2021.e06212
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author Blé, Gamaliel
Castellanos, Víctor
Castillo-Santos, Francisco Eduardo
author_facet Blé, Gamaliel
Castellanos, Víctor
Castillo-Santos, Francisco Eduardo
author_sort Blé, Gamaliel
collection PubMed
description In this paper we analyze the dynamics of a tritrophic food chain, with functional responses of Holling type III and II for the mesopredator and superpredator respectively and logistic growth rate for the prey. We show that there are parameter conditions for which the system has up to three equilibrium points. When three equilibrium points appear we show that each one of them exhibits a supercritical Hopf bifurcation. Moreover we can also show that there is a set of parameters for which the system exhibits a simultaneous Hopf bifurcation.
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spelling pubmed-79025552021-03-03 Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses Blé, Gamaliel Castellanos, Víctor Castillo-Santos, Francisco Eduardo Heliyon Research Article In this paper we analyze the dynamics of a tritrophic food chain, with functional responses of Holling type III and II for the mesopredator and superpredator respectively and logistic growth rate for the prey. We show that there are parameter conditions for which the system has up to three equilibrium points. When three equilibrium points appear we show that each one of them exhibits a supercritical Hopf bifurcation. Moreover we can also show that there is a set of parameters for which the system exhibits a simultaneous Hopf bifurcation. Elsevier 2021-02-17 /pmc/articles/PMC7902555/ /pubmed/33665414 http://dx.doi.org/10.1016/j.heliyon.2021.e06212 Text en © 2021 Published by Elsevier Ltd. http://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Research Article
Blé, Gamaliel
Castellanos, Víctor
Castillo-Santos, Francisco Eduardo
Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses
title Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses
title_full Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses
title_fullStr Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses
title_full_unstemmed Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses
title_short Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses
title_sort bistability and hopf bifurcation of a tritrophic system with holling functional responses
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7902555/
https://www.ncbi.nlm.nih.gov/pubmed/33665414
http://dx.doi.org/10.1016/j.heliyon.2021.e06212
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