A Reaction-diffusion Predator-prey System In Spatial Heterogeneous Environment

In this paper,we mainly study a reaction-diffusion predator-prey model in het-erogeneous space environment.Diffusion and heterogeneous space environment will affect the stability of population.By linearizing the model,we study the principal eigenvalue symbols of eigenvalue problem and obtain the stability of semi-trivial solution under different conditions.Finally,we obtain the steady state by a priori estimate of semi-trivial steady-state solution.The bifurcation value,the direction and uniqueness of the bifurcation value,and the stability of the bifurcation solution of the system are discussed.