Andronov-Hopf and Bautin bifurcation in a tritrophic food chain model with Holling functional response types IV and II

Blé, Gamaliel and Castellanos, Víctor and Loreto-Hernández, Iván: Andronov-Hopf and Bautin bifurcation in a tritrophic food chain model with Holling functional response types IV and II. Electronic journal of qualitative theory of differential equations 78. pp. 1-27. (2018)

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Abstract

The existence of an Andronov–Hopf and Bautin bifurcation of a given system of differential equations is shown. The system corresponds to a tritrophic food chain model with Holling functional responses type IV and II for the predator and superpredator, respectively. The linear and logistic growth is considered for the prey. In the linear case, the existence of an equilibrium point in the positive octant is shown and this equilibrium exhibits a limit cycle. For the logistic case, the existence of three equilibrium points in the positive octant is proved and two of them exhibit a simultaneous Hopf bifurcation. Moreover the Bautin bifurcation on these points are shown.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 78
Page Range: pp. 1-27
ISSN: 1417-3875
Uncontrolled Keywords: Matematikai modell, Bifurkáció
Additional Information: Bibliogr.: p. 26-27. ; Összefoglalás angol nyelven
Date Deposited: 2018. Nov. 07. 13:05
Last Modified: 2018. Nov. 07. 13:05
URI: http://acta.bibl.u-szeged.hu/id/eprint/55748

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