Coexistence Of Two Types Of Food Web Model

In this paper, we mainly discuss co-existence states of population ecology. Co-existence states of population is an important branch of biomathematics, also.it is recently active subjuct in ecology. In the past few decades, reseachers have made great achievements in co-existence states of population ecology. Recently, some biologists and mathematicians have devoted themselves to reseach this problem.In the third boundary value conditions, by using of reaction diffusion equations and theories of nonlinear anatysis, we will discuss co-existence states for a food web in an un-stirred Chemostat and coexistence states of food web model with ratio-dependent where Then, we analysis and study the existence and stability of steady-state solution by using the fixed point index, and in combination with the comparison principle, extremum principle, upper and lower solution and spectral analysis of operators. The mainly contents in this paper are as follows:In chapter 1, we reseach the existence of the positive steady-state solution to the un-stirred food-chain Chemostat model with Beddington-DeAngelis functional reponse, this model includes one prey and two predators populations besides nutri-ent. This chapter consists of two parts:In the first part, we obtain prior estimate of steady-state solution by using partial differential equations; In the second part, we establish the necessary and sufficient condition of the existence of positive steady-state by using dancer fixed pointed index and the degree theory.In chapter 2, we study coexistence states of food web model with ratio-dependent, this model comprises two competitive prey species and a predator populations. This chapter consists of three parts:In the first part, existence and nonexistence of pos-itive solutions of the model are given by knowledge of degree theory and spectrum analysis of operators; In the second part, we discuss uniqueness and stability of coexistence states; In the third part, asymptotic behavior and global attractors of solution are shown.