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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 930762, 8 pages
http://dx.doi.org/10.1155/2014/930762
Research Article

Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays

School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, China

Received 25 January 2014; Accepted 14 May 2014; Published 26 May 2014

Academic Editor: Xinguang Zhang

Copyright © 2014 Nai-Wei Liu and Ting-Ting Kong. 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 predator-prey system with Beddington-DeAngelis functional response and delays, in which not only the stage structure on prey but also the delay due to digestion is considered. First, we give a sufficient and necessary condition for the existence of a unique positive equilibrium by analyzing the corresponding locations of a hyperbolic curve and a line. Then, by constructing an appropriate Lyapunov function, we prove that the positive equilibrium is locally asymptotically stable under a sufficient condition. Finally, by using comparison theorem and the -limit set theory, we study the global asymptotic stability of the boundary equilibrium and the positive equilibrium, respectively. Also, we obtain a sufficient condition to assure the global asymptotic stability.