Two Types Of Prey - Continuous Research Of The Model

The development of modern science and technology relies heavily on the achieve-ments and progress of biology, chemistry and physics, these disciplines precision is an important guarantee for progress. The exact discipline is often achieved through the establishment of the mathematical model, and a large number of mathemati-cal models can be summarized as the so-called reaction diffusion equations. The reaction diffusion equation is very important and is widely used for a class of par-tial differential equations, which describe the complex progress of the number of species of migratory ecology changes. In this paper, we discuss the bifurcation and stability of the positive constant equilibrium solution of two predator-prey models. Predator-prey model has been the research hotspot of ecological mathematics,in some ecosystems, the interaction between the population in the population diffusion plays a very important role.In this paper, we studies a class of predator-prey model with cross diffusionIn nature, many biological populations in a lifetime experience both juvenile and adult stages, for example, mammals and some amphibious. Therefore in this paper we studies the spatial distribution of species density nonuniformity in the case of prey with stage structure model where u, v, wrespectively juvenile prey, adult prey and predator population popu-lation density. In the model, the juvenile prey and adult prey transformation into each other and predator only to adult prey for food.The main contents in this paper are as follows:In chapter1, we reseach the bifurcation of the positive equilibrium solution and extend the local bifurcation solution to the global one to the predator-prey model with cross diffusion. This chapter consists of three parts:in the first part, we obtain prior estimate of equilibrium solution by using maximum principle; in the second part, we obtain local bifurcation of positive solutions by Crandall-Rabinowitz local bifurcation theory; in the three part, we extend the local bifurcation solution to the global one by using the global bifurcation theory.In chapter2, we study a predator-prey model with stage structure,in the model the prey will be divided into juvenile and adult stage, mainly discuss the steady of the positive constant solutions and the nonexistence of the non-constant positive solution. This chapter consists of three parts:in the first part, existence of the non-negative solutions of the model are given; in the second part, we discuss local asymptotic stability of the positive constant solution; in the third part, description of the model of constant positive solution does not exist.