Study On The Periodic Solution And Stability Of Several Ecosystem Systems

This paper consists of three parts:Firstly, we discuss a nonautonomous n-species two-patches cooperative Lotka-Volterra diffusion system. Using Brouwer fixed-point theory and Liapunov function, under some conditions, we obtain that the system has a unique globally asymptotically stable positive periodic solution.Secondly, we consider a kind of nonautonomous predator-prey model, in which preys are with stage structure and the predator are with two patches. With the help of comparison theorem, sufficient conditions which guarantee permanence of the system are obtained. For the almost periodic case, by constructing a suitable Liapunov function, we obtained that the system has a unique globally asymptotically stable positive almost periodic solution.Finally, we study a multispecies predator-prey system with stage structure and Holling Ⅱ type functional response. By constructing the suitable Liapunov function and using comparison theorem, under appropriate conditions, the result that the uniform persistence of the ecosystem is obtained. Further, if the ecosystem is periodic one, then it has a strictly positive periodic solution which is globally asymptotically stable.