Qualitative Analysis Of Three Species Prey-predator Model With Diffusion

In this paper, two predator-prey reaction-diffusion with three species model are considered.The paper is mainly divided into five chapters.The first section is the introduction of the whole paper. We talk about the background of this problem, and make plans for the research of the problems.The second cection mainly introduce some basic knowledge and correlated theorem.The third section of the paper mainly investigates the non-constant positive solution of the following model:We will obtain the non-existence and existence of non-constant positive solutions.The forth section mainly investigates the non-constant positive solution of the following model:We discuss the dissipation, persistence, the stability of the positive constant solution of this model. Moreover, non-existence and existence conditions for non-constant positive solution are given.At last, we summarize the results of the whole paper .