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Global stability and asymptotically periodic solution for nonautonomous cooperative Lotka-Volterra diffusion system. (English) Zbl 1113.92062
Summary: Two asymptotically cooperative Lotka-Volterra populations in a two-patch-system with diffusion are considered. Each population could diffuse independently and discretely between its intrapatches and interpatches. By means of constructing a suitable Lyapunov function, we obtain that the systems have a unique asymptotically periodic solution which is globally asymptotically stable.

MSC:
92D40Ecology
34D23Global stability of ODE
92D25Population dynamics (general)
34D20Stability of ODE
34D05Asymptotic stability of ODE
37N25Dynamical systems in biology