The Property Of Solutions In Multi-species Cooperating And Competitive Model

Using the upper and lower solutions, quasimonotone property in reaction-diffusion systems, this dissertation is concerned with global stability of equilibrium solutions for a class of multi-species cooperating model, the boundary conditions for the reaction-diffusion systems are homogeneous Neumann type. The unique, positive and constant stable solutions for this system are obtained. While, we also study a class of multi-species competitive model, the boundary conditions for the reaction-diffusion systems are also homogeneous Neumann type, the permanent solutions for these systems are obtained.The five chapters of this dissertation are as follows:In the fist chapter, the background of selecting this question is introduced briefly, while, the involved concepts and theorems in this dissertation are given.In the second chapter, we mainly study several biological models, and the characteristics of these solutions are briefly introduced.In the third chapters, we research the initial-boundary problems in these reaction-diffusion systems.In the fourth chapter, we study the global stability of equilibrium solutions for a class of multi-species cooperating model, the boundary conditions for the reaction-diffusion systems are homogeneous Neumann type. The unique, positive and constant stable solutions for this system are obtained.In the last chapter, we research a class of multi-species competitive model, the boundary conditions for the reaction-diffusion systems are also homogeneous Neumann type, and the permanent solutions for these systems are obtained.