Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 141272, 18 pages
http://dx.doi.org/10.1155/2012/141272
Research Article

Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response

Yanzhen Wang1 and Min Zhao2

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

Received 9 August 2011; Accepted 3 October 2011

Academic Editor: Elmetwally Elabbasy

Copyright © 2012 Yanzhen Wang 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 behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system is also confirmed. Furthermore, numerical analysis is used to discover the influence of impulsive perturbations. The system is found to exhibit rich dynamics such as symmetry-breaking pitchfork bifurcation, chaos, and nonunique dynamics.