Study On Several Population Dynamic Systems

This paper consists of three parts:We first consider the non-autonomous predator-prey system with both Beddirigton-DeAngelis functional response and dispersion. By using comparison theorem of differential equation, we study the permanance of the system. After that, by constructing suitable Lyapunov function, we obtain some sufficient condition which guarantee the existence of globally asymptotically stable almost periodic solution of the system.Next we study the Logistic model with both state-dependent delays and continuous delays and feedback control. With the help of coincidence degree theory, some new results for the existence of the postive periodic solution of the system are obtained. Also, by constructing suitable Lyapunov functional, some sufficient criteria for the uniqueness and globally asymptotic stability of positive periodic solution are established.Finally we study a predator-prey system with Holling II functional response and continuous infinite delay. With the help of coincidence degree theory, easily verifiable criteria are established for the global existence of positive periodic solutions of the system.