The Stability Of A Predator-prey Model With B-D Functional Response

In this paper, we study the stability of a predator-prey model with B-D functional response.In section 1, we discuss the stability of the predator-prey diffusion model with B-D functional response. The conditions of the stability of the ordinary differential system,the weak coupling reaction-diffusion system and the cross-diffusion system are given, and the global asymptotic stabilities of weakly coupled reaction-diffusion system are obtained by constructing Lyapunov function.In section 2, we study the stability of a predator-prey diffusion model with prey-taxis in one-dimensional space. Give the conditions of instability caused by prey-taxis, and the conditions of instability of the self-diffusion model with prey-taxis and the cross-diffusion model with prey-taxis.In section 3, we obtain the stability of a predator-prey diffusion model with prey-taxis in n-dimensional space. Give the conditions of instability caused by prey-taxis, and the conditions of instability of the self-diffusion model with prey-taxis and the cross-diffusion model with prey-taxis.