Specification Analysis Of Two Kinds Of Predator - Prey Model With Diffusion

This thesis mainly analyses the dynamical properties of two reaction-diffusion predator-prey system. As most of predators do not only feed on one single prey, but rather depend on alternative prey. In order to investigate the effect of alternative prey on the dynamics of predator-prey system, we study the following model: Taking into account the Allee effect on population growth, and the dependence of predation rate of predator on the population of prey species, we study another diffusion predator-prey model with strong Allee effect and ratio dependent functional response function.The main contents in this thesis are as follows:In chapter 1, we introduce the biological background and present research situ-ation on the two sorts of predator-prey model with diffusion, and some preliminary knowledge needed in this thesis.In chapter 2, the properties of positive steady-state solutions of a two species predator-prey model with alternative prey is discussed. Firstly, we analysis the stability condition of positive constant equilibrium; Then the existence of positive steady-state solutions is obtained by means of bifurcation theory, which with nu-merical simulation shows that the two species can continue to coexist in certain conditions.In chapter 3, we study the influence of strong Allee effect and ratio depen-dent functional response on the sustainability of species. A priori estimate of the positive steady-state solutions of the system is given by means of the maximum principle, then we taking d as a bifurcation parameter, the existence of local bi-furcation from semi-trivial solutions (u2*,0) is observed by using bifurcation theory and Leray-Schauder degree theory, and the local bifurcation can be extended to global bifurcation. What’s more, we discuss the locally asymptotical stability of the bifurcation solutions.