Predatorprey model of a stage structured impulse delay HollingII functional response

in which predator（natural enemy ）is released impulsively and the prey has stage structured and maturation time delay are discussed

and a systematic mathematical and ecological study are performed. Using the discrete dynamical system determined by the stroboscopic map

we obtain the existence of pesteradication periodic solution. And show that the pesteradication periodic solution is unique and globally attractive by using the basis of impulse and delay differential equation. Further

we prove that if the pulse releasing rate or impulsive period for natural enemy is within an appropriate range

the pest population can be controlled under the economic injury level(EIL)E

that is

the pest population and the natural enemy population may coexist. The results provide reliable tactical basis for the practical pest management.