Global dynamics on a circular domain of a diffusion predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional type

Walid  Abid; Radouane  Yafia; M.A.  Aziz-Alaoui; Habib  Bouhafa; Azgal  Abichou

doi:10.3934/eect.2015.4.115

Article Contents

2015, Volume 4, Issue 2: 115-129. Doi: 10.3934/eect.2015.4.115

This issue Previous Article Preface Next Article On observers and compensators for infinite dimensional semilinear systems

Global dynamics on a circular domain of a diffusion predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional type

1.
University of Tunis El Manar, National Engineering School of Tunis, Laboratory of Engineering Mathematics EPT, B.P 743, La Marsa 2078
2.
Ibn Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P: 638, Ouarzazate
3.
Normandie Univ, France; ULH, LMAH, F-76600 Le Havre; FR CNRS 3335, ISCN, 25 rue Philippe Lebon 76600 Le Havre

Received: April 30, 2014

Revised: September 30, 2014

Published: May 2015

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Abstract

In this paper, we present a predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response. The model is governed by a two dimensional reaction diffusion system defined on a disc domain. The conditions of boundedness, existence of a positively invariant and attracting set are proved. Sufficient conditions of local and global stability of the positive steady state are established. In the end, we carry out some numerical simulations in order to illustrate our theoretical results and to interpret how biological processes affect spatio-temporal pattern formation.

Keywords:

Beddington-DeAngelis functional response,
local and global stability,
pattern formation,
chaos,
disc domain.

Mathematics Subject Classification: Primary: 35Kxx, 35Pxx, 35Exx; Secondary: 35B32, 35B35, 35B36, 35B51.

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