Study On Several Population Dynamic Systems With Feedback Controls

This paper consists of four parts:We first consider a "pure-delay-type" single species population dynamics with feedback control and time-varying discrete delay. By constructing a suitable Lyapunov functional, sufficient condtions are obtained which guarantee the global attracitivity of the system.Secondly, we study a competitive system with feedback controls and toxic substance. By combinning with the comparison theorem of differential equation, Lyapunov function, and some subtly analysis, some average conditions for the permanence and global attractivity of the system are obtained.Thirdly, we study n-species Gilpin-Ayala competitive system with feedback controls. By introducing a new transformation, we change the system to a new system, and to investigate the almost periodic solution of the system, it's enough to investigate the almost periodic solution of the new system; After that, by using comparison theorem of differential equation and constructing a suitable Lyapunov function, sufficient condtions are obtained to guarantee the existence of a positive almost periodic solution of the system.Finally, we study the n-species cooperation system with discrete time delays and feedback controls. By using the comparison theorem of differential equation, we study the permanance of the system; After that, by constructing sutiable Lyapunov functional, we obtain some sufficient condition which guarantee the global attractivity of the system.