No abstract

In this paper, on the basis of the theories and methods of ecology and ordinary differential equations, an ecological Gompertz model with Holling III functional response and stage structure for predator is established. By use of the stroboscopic map, a predator extinction periodic solution is obtained, and the global attractivity of the predator extinction periodic solution is analyzed. By using comparison theorem of impulsive differential equation and small amplitude perturbation skills, we get the sufficient condition for permanence of the system under impulsive harvest strategy for the prey and maturation time delay of predator.