Study On The Permanence And Stability Of Several Population Dynamic Systems

This paper consists of four parts:Firstly, we consider a non-autonomous nonlinear growth rate Logistic model with time delays. By using the comparison theorem, sufficient conditions which guarantee the permanence of the system are obtained. For the almost periodic case, by constructing a suitable Lyapunov function, sufficient conditions are established for the existence of almost periodic solution of the system.Secondly, we study a non-autonomous nonlinear growth rate single-species dispersal model with time delays. With the help of the comparison theorem and by analysising the right-hand side functional directly, sufficient conditions which guarantee the permanence or extinction of the system are obtained. An interesting result is established, that is, if only the species in some patches even in one patch is permanent, then it is also permanent in other patches. Examples together with their numerical simulations show that our main results are easily verifiable, general and feasible.Thirdly, we study a multi-species nonlinear prey-competition system with almost periodic coefficient. By analysising the right-hand side expression strictly, sufficient conditions which guarantee the permanence of the system are established.Finally, a single species population dynamics with feedback control and finite continuous delays is proposed. By constructing a suitable Lyapunov functional, sufficient condition are obtained to guarantee the global attracitivity of the system.