Abstract: Considering the impulsive effects at different fixed moments and the predator stage-structure, we propose a three species predator-prey system with predator stage-structure and impulsive effects in this paper. At first, we prove the existence, stability and global attractivity of the prey-extinction periodic solution via the Floquent theory and small amplitude perturbation. Then, we obtain the permanence of this system by using comparison method and involving multiple Laypunov functions. Finally, we show our theoretical results by numerical simulations, such as time series of species population and chaotic bands of system.

Key words: stage-structure, impulsive, permanence, numerical simulation