Abstract and Applied Analysis
Volume 2012 (2012), Article ID 183285, 25 pages
http://dx.doi.org/10.1155/2012/183285
Research Article

Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers

Yujuan Jiao1,2 and Shengmao Fu1

1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, China

Received 23 March 2012; Accepted 15 May 2012

Academic Editor: Michiel Bertsch

Copyright © 2012 Yujuan Jiao and Shengmao Fu. 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 consider a strongly coupled predator-prey model with one resource and two consumers, in which the first consumer species feeds on the resource according to the Holling II functional response, while the second consumer species feeds on the resource following the Beddington-DeAngelis functional response, and they compete for the common resource. Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for the model are proved. Meanwhile, the sufficient conditions for global asymptotic stability of the positive equilibrium for this model are given by constructing a Lyapunov function.