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

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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Main Authors: Gamaliel Blé, Víctor Castellanos, Francisco Eduardo Castillo-Santos
Format: Article
Language:English
Published: Elsevier 2021-02-01
Series:Heliyon
Subjects:
Hopf bifurcation
Limit cycle
Tritrophic model
Online Access:http://www.sciencedirect.com/science/article/pii/S2405844021003170
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spelling doaj-24cbba7c1f024ac280f13923f001f0fc2021-03-03T04:24:12ZengElsevierHeliyon2405-84402021-02-0172e06212Bistability and Hopf bifurcation of a tritrophic system with Holling functional responsesGamaliel Blé0Víctor Castellanos1Francisco Eduardo Castillo-Santos2UJAT, CONACYT-UJAT, División Académica de Ciencias Básicas, Km 1, Carretera Cunduacán–Jalpa de Méndez, c.p. 86690, Cunduacán, Tabasco, MexicoCorresponding author.; UJAT, CONACYT-UJAT, División Académica de Ciencias Básicas, Km 1, Carretera Cunduacán–Jalpa de Méndez, c.p. 86690, Cunduacán, Tabasco, MexicoUJAT, CONACYT-UJAT, División Académica de Ciencias Básicas, Km 1, Carretera Cunduacán–Jalpa de Méndez, c.p. 86690, Cunduacán, Tabasco, MexicoIn 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.http://www.sciencedirect.com/science/article/pii/S2405844021003170Hopf bifurcationLimit cycleTritrophic model
collection DOAJ
language English
format Article
sources DOAJ
author Gamaliel Blé
Víctor Castellanos
Francisco Eduardo Castillo-Santos
spellingShingle Gamaliel Blé
Víctor Castellanos
Francisco Eduardo Castillo-Santos
Bistability and Hopf bifurcation of a tritrophic system with Holling functional responses
Heliyon
Hopf bifurcation
Limit cycle
Tritrophic model
author_facet Gamaliel Blé
Víctor Castellanos
Francisco Eduardo Castillo-Santos
author_sort Gamaliel Blé
title 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_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_sort bistability and hopf bifurcation of a tritrophic system with holling functional responses
publisher Elsevier
series Heliyon
issn 2405-8440
publishDate 2021-02-01
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.
topic Hopf bifurcation
Limit cycle
Tritrophic model
url http://www.sciencedirect.com/science/article/pii/S2405844021003170
work_keys_str_mv AT gamalielble bistabilityandhopfbifurcationofatritrophicsystemwithhollingfunctionalresponses
AT victorcastellanos bistabilityandhopfbifurcationofatritrophicsystemwithhollingfunctionalresponses
AT franciscoeduardocastillosantos bistabilityandhopfbifurcationofatritrophicsystemwithhollingfunctionalresponses
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