ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Global Dynamics of a Three Species Predator-Prey Competition Model with Holling type II Functional Response on a Circular Domain

Journal of Applied Nonlinear Dynamics 5(1) (2016) 93--104 | DOI:10.5890/JAND.2016.03.007

Walid Abid$^{1}$, R. Yafia$^{2}$, M.A. Aziz-Alaoui$^{3}$, H. Bouhafa$^{1}$, A. Abichou$^{1}$

$^{1}$ Université de Carthage, Laboratoire d’ingenierie Mathématique EPT, Tunisia

$^{2}$ Ibn Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P: 638, Ouarzazate, Morocco

$^{3}$ Laboratoire de Mathématiques Appliquées, 25 Rue Ph. Lebon, BP 540, 76058Le Havre Cedex

Abstract

This paper is devoted to the study of a three species ecosystem model consisting of a prey, a predator and a top predator. This model is given by a reaction diffusion system defined on a circular spatial domain and incorporates the Holling type II and a modified Leslie- Gower functional response. The aim of this paper is to investigate theoretically and numerically the asymptotic behavior of the interior equilibrium of the model. The conditions of boundedness, existence of a positively invariant and attracting set are proved. Sufficient conditions of local/global stability of the positive steady state are established. In the end, we present a numerical evidence of time evolution of the pattern formation.

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