Abstract: Established in this paper is a time-delay predator-prey-environment model with stage structure of predator, impulsive harvesting of prey and impulsive input of pollutant in polluted environment. By using the stroboscopic mapping and the comparison principle of discrete dynamical systems, sufficient conditions for the global attractiveness of the predator extinction periodic solution and system persistence are obtained. Through numerical simulation, the effects of the prey capture, pulse input of pollutants and pulse action period on the extinction and survival of predators are studied, and the theoretical results are verified. It provides valuable theoretical basis for the development of biological resources, the harvest of population number and the control of environment.

Key words: impulsive harvesting, stage structure, pulse input for pollutant, predator-prey-environment model, extinction periodic solution, persistence