Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 256195, 15 pages
doi:10.1155/2009/256195

A predator-prey Gompertz model with time delay and impulsive perturbations on the prey

Abstract

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.