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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 256195, 15 pages
Research Article

A Predator-Prey Gompertz Model with Time Delay and Impulsive Perturbations on the Prey

School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, China

Received 28 June 2009; Accepted 5 November 2009

Academic Editor: Leonid Berezansky

Copyright © 2009 Jianwen Jia and Chunhua Li. 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.


We introduce and study a Gompertz model with time delay and impulsive perturbations on the prey. By using the discrete dynamical system determined by the stroboscopic map, we obtain the sufficient conditions for the existence and global attractivity of the “predator-extinction” periodic solution. With the theory on the delay functional and impulsive differential equation, we obtain the appropriate condition for the permanence of the system.