Study On The Permanence And Extinction Of Several Population Dynamic Systems

In this paper, we consider four kinds of population dynamic systems:Firstly, we study a predator-prey system with stage-structure and functional response, we obtain sufficient condition for the strong persistence of the proposed ecological system; by constructing a suitable Lyapunov function, some sufficient conditions which guarantee nonnegative verge equilibrium to be global asympototics stability are obtained.Secondly, we study a periodic Holling type-IV predator-prey system with stage structure for prey. Under certain assumptions, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.Thirdly, we study a delayed discrete ratio-dependent predator-prey model with monotonic functional responses. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system; also, we obtain sufficient condition for extinction of the predator.Finally, we study a discrete nonlinear n-species competition system with time delays and feedback controls. With the help of the comparison theorem of difference equation and some subtly analysis, sufficient conditions are obtained for the permanence of the system.