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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.

34D23Global stability of ODE
92D25Population dynamics (general)
34D20Stability of ODE
34D05Asymptotic stability of ODE
37N25Dynamical systems in biology
Full Text: DOI
[1] Zhixiang, Li: The application of Liapunov method in research of almost periodic system (I). Chinese science bulletin 809, No. 12, 4-9 (1989)
[2] Chongyou, He: Almost periodic differential equation. (1992)
[3] Changhong, Liu; Lansun, Chen: Periodic solution and global stability for nonautonomous cooperative Lotka -- Volterra diffusion system. Journal of Lanzhou university (Natural science) 33, 33-37 (1997)
[4] Fengying, Wei; Ke, Wang: Almost periodic solution and stability for nonautonomous cooperative Lotka -- Volterra diffusion system. Songliao journal (Natural science edition) 3, 1-4 (2002)