The Study On Nonautonomous Predator-prey Systems With Stage-structure

In this paper, we study some nonautonomous predator-prey systems with stage-structured. We discuss periodic solution, permanence and global asymptotic stability of population ecological model. The article is divided into four chapters.In Chapter 1, we introduce some knowledge of biology mathematics and some prelimineries.In Chapter 2, we study a predator-prey model with stage-structured and predator has ratio-dependent functional response. We obtain the sys-tem can persistence under certain conditions. By using comparison theo-rem we obtain some sufficient conditions for the permannence of system.In Chapter 3, we study a nonautonomous predator-prey model with time delay and stage-structured. By using comparison theorem we prove the permannence of system. We also obtain sufficient conditions for the existence of positive periodic solution by using coincidence degree theory.In Chapter 4, we introduce a stage-structured model with time delay and impulsive perturbations on the prey. We discuss the boundedness of model. By using the theory on delay impulisive differential equation, we show the existence and global attractivity of the predator-extinction periodic solution of the system.