Dynamical analysis of a stage structured predator-prey system with impulsive diffusion and generic functional response

Based on the predator-prey system with stage structure and generalized functional response, an impulsive differential system to model the process of periodical diffusion at different fixed time is proposed and investigated. By using comparison theorem of impulsive differential equation and some analysis techniques, sufficient conditions ensuring the existence of a predator-extinction positive periodic solution and the permanence of the system are established. Numerical simulation shows that impulses and functional response affect the dynamics of the system, which may be very complex.