Ecosystem Dynamics Analysis With Holling ? Type Functional Response And Diffusion

In this paper,the stability behavior of three kinds of non-autonomous predator-prey dynamical systems with Holling ? type functional response and diffusion is studied.The three kinds of systems are analyzed,and the sufficient conditions for the persistence of the system and the global stability of periodic solutions are obtained,and the correctness of some conclusions is verified by numerical simulation.In chapter one,we mainly introduce the research background,the present situation and the preparatory knowledge of the predator-prey system with a functional response of Holling ? and diffusion.In chapter two,we study a class of non-autonomous predator-prey systems with diffu-sion and Holling ? functional response.By using the comparison theorem,the sufficient conditions for the uniform persistence of the system are given.When the system is a peri-odic system,by constructing a Liapunov function,the sufficient conditions for the existence of a globally stable positive periodic solution for the system are obtained.In chapter three,we study a three-species predator-prey system with a nonlinear diffu-sion and competition relation of prey population,a predator with continuous and discrete delays,and Holling ?type functional response.By using the comparison theorem,the sufficient conditions for the uniform persistence of the system are obtained.By using the Brouwer fixed point theorem and the construction of the Liapunov function,the sufficient conditions for the existence,uniqueness and global stability of positive periodic solutions of corresponding periodic systems are obtained.In chapter four,we study a kind of predator-prey system with diffusion and shelter effect,which is predatory by predators with stage structure and delay,and has a function-al response of Holling ?.By using the comparison theorem,it is proved that the system is uniformly persistent under appropriate conditions,and by constructing the Liapunov function,the sufficient conditions for the existence of a globally stable positive periodic solution of the system are obtained.Finally,the correctness of the conclusion is verified by numerical simulation.