Global stability and asymptotically periodic solution for nonautonomous cooperative Lotka–Volterra diffusion system

Two asymptotically cooperative Lotka–Volterra populations in the two-patch-system with diffusion were considered in this paper. Each population could diffuse independently and discretely between its intrapatch and interpatch. By means of constructing a suitable Liapunov function, we obtained that the systems had a unique asymptotically periodic solution which was globally asymptotically stable.