Global Asymptotic Behavior of N-Patches Nonautonomous Predator-Prey System with Nonlinear Diffusion

In this paper, we investigate a n-patches nonautonomous predator-prey system with nonlinear diffusion. By the comparison theorem, the sufficient conditions are derived for uniform persistence of the system. We also prove the existence of positive periodic solution of the system by using Schauder´s fixed point theorem. Furthermore, the sufficient conditions for global asymptotical stability of positive periodic solution are obtained by constructing an appropriate Lyapunov function. The conditions we obtained are more general. We also give the ecology interpretation to our results.