Existence of limit cycles in a tritrophic food chain model with Holling functional responses of type II and III

Gamaliel Blé; Víctor Castellanos; Jaume Llibre

doi:10.1002/mma.3842

Existence of limit cycles in a tritrophic food chain model with Holling functional responses of type II and III

Gamaliel Blé, Víctor Castellanos, Jaume Llibre

Departament de Matemàtiques

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Resum

Copyright © 2016 John Wiley & Sons, Ltd. We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species, Holling III and Holling II functional response for the predator and the top-predator, respectively. We prove that this model has stable periodic orbits for adequate values of its parameters. Copyright © 2016 John Wiley & Sons, Ltd.

Idioma original	Anglès
Pàgines (de-a)	3996-4006
Revista	Mathematical Methods in the Applied Sciences
Volum	39
Número	14
DOIs	https://doi.org/10.1002/mma.3842
Estat de la publicació	Publicada - 30 de set. 2016

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10.1002/mma.3842

https://ddd.uab.cat/record/221042

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title = "Existence of limit cycles in a tritrophic food chain model with Holling functional responses of type II and III",

abstract = "Copyright {\textcopyright} 2016 John Wiley & Sons, Ltd. We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species, Holling III and Holling II functional response for the predator and the top-predator, respectively. We prove that this model has stable periodic orbits for adequate values of its parameters. Copyright {\textcopyright} 2016 John Wiley & Sons, Ltd.",

keywords = "Hopf bifurcation, Lyapunov coefficient, periodic orbit, population dynamics",

author = "Gamaliel Bl{\'e} and V{\'i}ctor Castellanos and Jaume Llibre",

year = "2016",

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T1 - Existence of limit cycles in a tritrophic food chain model with Holling functional responses of type II and III

AU - Blé, Gamaliel

AU - Castellanos, Víctor

AU - Llibre, Jaume

PY - 2016/9/30

Y1 - 2016/9/30

N2 - Copyright © 2016 John Wiley & Sons, Ltd. We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species, Holling III and Holling II functional response for the predator and the top-predator, respectively. We prove that this model has stable periodic orbits for adequate values of its parameters. Copyright © 2016 John Wiley & Sons, Ltd.

AB - Copyright © 2016 John Wiley & Sons, Ltd. We are interested in the coexistence of three species forming a tritrophic food chain model. Considering a linear grow for the lowest trophic species, Holling III and Holling II functional response for the predator and the top-predator, respectively. We prove that this model has stable periodic orbits for adequate values of its parameters. Copyright © 2016 John Wiley & Sons, Ltd.

KW - Hopf bifurcation

KW - Lyapunov coefficient

KW - periodic orbit

KW - population dynamics

U2 - 10.1002/mma.3842

DO - 10.1002/mma.3842

M3 - Article

SN - 0170-4214

VL - 39

SP - 3996

EP - 4006

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 14

ER -

Existence of limit cycles in a tritrophic food chain model with Holling functional responses of type II and III

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