Permanence of a Delayed Predator-Prey Model with Stage-Structure and Holling II Functional Response

Considering the prey is a linear growth and is impulsively harvest, in this paper a predator-prey model with a stage structure for the predator which improves the assumption that each individual predator has the same ability to capture prey is proposed. It is assumed that immature individuals and mature individuals of the predator are divided by a fixed age and that immature predator do not have the ability to attach prey. By using the comparison theorem in impulsive differential equation,we obtain that when the death rate of the mature predator is less than the critical value and the impulsive period is larger than some critical value,the system is shown to be permanent, Our results indicate that the permanence of the system depends on impulsive perturbation.