Title: Spatiotemporal dynamics of a predator-prey system with Beddington-DeAngelis functional response and the modified Leslie-Gower type dynamics incorporating prey refuge

Authors: Dawit Melese; Sunita Gakkhar

Addresses: Department of Mathematics, Arba Minch University, P.O. Box 21, Arba Minch, Ethiopia ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India

Abstract: In this paper, a spatial predator-prey system with Beddington-DeAngelis functional response and the modified Leslie-Gower type dynamics incorporating constant proportion of prey refuge under homogeneous Neumann boundary condition is considered. The qualitative properties, including the persistence property, local and global asymptotic stability of the unique positive homogeneous steady state are discussed. Furthermore, a series of numerical simulations are performed and the results of the numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripe like or spotted or coexistence of both. The results indicate that the effect of the prey refuge for pattern formation is remarkable. More specifically, as the value of the prey refuge constant is increased, the stripe like patterns breaks down and ultimately form spotted like patterns.

Keywords: prey refuge; diffusion driven instability; Turing patterns; modified Leslie-Gower dynamics; Beddington-DeAngelis functional response; predator-prey dynamics; numerical simulation; pattern formation.

DOI: 10.1504/IJMMNO.2013.051335

International Journal of Mathematical Modelling and Numerical Optimisation, 2013 Vol.4 No.1, pp.71 - 90

Received: 18 Mar 2012
Accepted: 31 Jul 2012

Published online: 05 Jan 2013 *

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