Stability And Traveling Waves Of Diffusive Predator-prey Model With Stage Structure

Population biology has developed widely as one important component in mathe-matical biology on recent years,and predator-prey model is one of the basic models in population biology.In the nature world,there are many species whose individuals have a life history that takes them through two stages:immature and mature,and species at two stages may have different behaviors,therefore this paper is purported to study a reaction diffusion predator-prey with stage structure.The full text is divided into four sections. The first section-outlines the background.In the second section,the stability of the equilibria is investigated by using the characteristic equation technique.Section Ⅲ, a pair of upper-lower solutions is constructed by using in-equality technique and characteristic equations.Section Ⅳ,by constructing a closed convex set bounded by a pair of upper-lower solutions and using Schauder fixed pointed theo-rem,the existence of traveling wave solution connecting two steady states is also derived.