Differential Equations and Nonlinear Mechanics
Volume 2010 (2010), Article ID 813289, 24 pages
doi:10.1155/2010/813289
Research Article

Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response

Wahiba Khellaf1 and Nasreddine Hamri2

1Laboratory of LMPA, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel, Algeria
2Laboratory Math, University of Mentouri, 25000 Constantine, Algeria

Received 17 September 2009; Accepted 19 April 2010

Academic Editor: Bhabani Shankar Dandapat

Copyright © 2010 Wahiba Khellaf and Nasreddine Hamri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.