Persistence Analysis And Optimal Harvesting Of Predator-prey System With Machaelis-menten Functional Response

In this paper, the stability behavior of four predator-prey systems with Machaelis-Menten functional response are investigated. By analyzing the four models in the paper,we mainly obtain the sufficient conditions for permanence of the system and global stability of positive periodic solution, and present numerical simulation to validate some conclusions.In chapter one, we mainly introduce the current background and situation, some corresponding main definitions and theorems about predator-prey model with Machaelis-Menten functional response.In chapter two, a ratio-dependent nonautonomous predator-prey model with Machaelis-Menten functional response and diffusion is investigated in this paper. The sufficient con-ditions for the persistence of system are obtained by comparative principle. Also, when the system is periodic, some sufficient conditions for the existence and asymptotic stability of a periodic solution of the system is given through constructing a Liapunov function.In chapter three, a predator-and-two-competitive-prey model with stage structure and Machaelis-Menten functional response for predator is investigated. Using comparison theorem, the permanence and extinction of the system are obtained. Further, for the periodic case, a set of sufficient conditions for the existence and global asymptotic stability of a periodic solution is presented through Brouwer theorem and constructing a Liapunov function.In chapter four, a two-predator-and-two competitive-prey system with Machaelis-Menten Functional Response for the predator is investigated. Using comparison theorem,the permanence of the system is obtained. The sufficient conditions for the global asymp-totic stability of the system are presented through constructing a Liapunov function. At the end, a set of sufficient conditions is proved, which guarantee the existence, uniqueness and global asymptotic stability of a positive periodic solution.In chapter five, we analyze a predator-prey system of harvesting at the time which is with time delay, stage structure and Machaelis-Menten functional response. By using comparison theorem, the sufficient conditions for the global asymptotic stability of the system's equilibrium solutions are presented. In addition, we derive the optimal sustained yield and maximal harvesting yield with objective of maximal sustained yield in different conditions.