Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 724014, 19 pages
http://dx.doi.org/10.1155/2012/724014
Research Article

Mathematical and Dynamic Analysis of a Prey-Predator Model in the Presence of Alternative Prey with Impulsive State Feedback Control

Chuanjun Dai1 and Min Zhao2

1School of Mathematics and Information Science, Wenzhou University, Zhejiang, Wenzhou 325035, China
2School of Life and Environmental Science, Wenzhou University, Zhejiang, Wenzhou 325035, China

Received 5 October 2011; Revised 21 December 2011; Accepted 21 February 2012

Academic Editor: Xue He

Copyright © 2012 Chuanjun Dai and Min Zhao. 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

The dynamic complexities of a prey-predator system in the presence of alternative prey with impulsive state feedback control are studied analytically and numerically. By using the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions can be obtained. Furthermore, the corresponding bifurcation diagrams and phase diagrams are investigated by means of numerical simulations which illustrate the feasibility of the main results.