Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 716932, 17 pages
doi:10.1155/2010/716932
Research Article

The Effect of Impulsive Diffusion on Dynamics of a Stage-Structured Predator-Prey System

Jianjun Jiao1,2

1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
2Guizhou Key Laboratory of Economic System Simulation, Guizhou College of Finance and Economics, Guiyang 550004, China

Received 6 June 2010; Accepted 13 September 2010

Academic Editor: Antonia Vecchio

Copyright © 2010 Jianjun Jiao. 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 investigate a predator-prey model with impulsive diffusion on predator and stage structure on prey. The globally attractive condition of prey-extinction periodic solution of the system is obtained by the stroboscopic map of the discrete dynamical system. The permanent condition of the system is also obtained by the theory of impulsive delay differential equation. The results indicate that the discrete time delay has influence on the dynamical behaviors of the system. Finally, some numerical simulations are carried out to support the analytic results.