Journal of Applied Mathematics
Volume 2012 (2012), Article ID 534276, 17 pages
http://dx.doi.org/10.1155/2012/534276
Research Article

Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control

Chuanjun Dai,1 Min Zhao,2 and Lansun Chen3

1School of Mathematics and Information Science, Wenzhou University, Zhejiang, Wenzhou 325035, China
2School of Life and Environmental Science, Wenzhou University, Zhejiang, Wenzhou 325035, China
3Institute of Mathematics, Academia Sinica, Beijing 100080, China

Received 19 January 2012; Revised 17 April 2012; Accepted 8 May 2012

Academic Editor: Huijun Gao

Copyright © 2012 Chuanjun Dai et al. 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 an Ivlev-type prey-predator system with impulsive state feedback control are studied analytically and numerically. Using the analogue of the Poincaré criterion, sufficient conditions for the existence and the stability of semitrivial periodic solutions can be obtained. Furthermore, the bifurcation diagrams and phase diagrams are investigated by means of numerical simulations, which illustrate the feasibility of the main results presented here.