Study On The Dynamic Behaviors Of Four Kinds Of Nonautonomous Predator-Prey System Incorporating A Prey Refuge

This paper consists of four parts:Firstly, we propose and study a nonautonomous discrete predator-prey system incorporating a prey refuge and Holling type II functional response. By applying a difference inequality, we obtain a set of sufficient conditons which guarantee the persistence, global stability and the extinction of predator of the system.Secondly, we study the extinction of predator species in a nonautonomous predator-prey system incorporating time varying prey refuge. In order to overcome the difficulties that we cannot directly use the comparison theorem of differential equation to analysis the dynamic behaviors of the system, we develop the idea of the oscillation theorey and the technique of classified discussion, then a set of sufficient conditions which ensure the extinction of the predator of the system are obtained. To the best of our knowledge, this is the first time that such kind of analysis techniques are explored to investigate the effect of refuge on the dynamic behaviors of predator-prey system. Our results show that large refuge will directly lead the predator to extinction due to the lack of enough food.Thirdly, we study the dynamic behavior of a nonautonomous predator-prey system incorporating a prey refuge and Rosenzweig functional response. By applying the comparison theorem of differential equations and the oscillation theorey, sufficient conditions which guarantee the permanence of the system and the extinction of the predator are obtained, respectively.Finally, we study the dynamic behavior of a nonautonomous modified Leslie-Gower predator-prey system incorporating a prey refuge. By applying the comparison theorem of differential equations, we obtain a set of sufficient conditions which guarantee the permanence of the system. Also, by constructing a suitable Lyapunov function, a set of sufficient conditions which guarantee the global stability of the system is obtained. Our study shows that the increase of the refuge can increase the chance of survival of prey species and finally increase the persistent property of the system.