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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)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

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

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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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