Journal of Applied Mathematics
Volume 2012 (2012), Article ID 607105, 17 pages
http://dx.doi.org/10.1155/2012/607105
Research Article

Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control

Chunjin Wei1 and Lansun Chen2

1Science College, Jimei University, Fujian, Xiamen 361021, China
2Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China

Received 18 June 2012; Revised 31 August 2012; Accepted 2 September 2012

Academic Editor: Shiping Lu

Copyright © 2012 Chunjin Wei and Lansun Chen. 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

A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results.