Stability And Instability In A Predator-prey Diffusion Model With B-D Functional Response

In this paper, we study the stability and instability of nonnegative constant equilibria in a predator-prey diffusion model with Beddington-DeAngelis functional response. First, we study the stability and instability of nonnegative constant equi-libria and the existence of bifurcation in the ODE system. Second, we investigate the stability and instability of nonnegative constant equilibria and the existence of bifurcation in the linear self-diffusion system. Third, we discuss the stability and in-stability of positive equilibrium point in the cross-diffusion system. The results show that cross-diffusion can not only destabilize an equilibrium point which is stable for the ODE system and linear self-diffusion system, but also stabilize an equilibrium point which is stable for the ODE system but unstable for the linear self-diffusion system. Finally, the sufficient conditions for the chemotaxis-driven instability of positive equilibrium point are demonstrated.