Stability Analysis Of Predator-Prey System With Impulse And Ivlev Functional Response Function

In this paper,three predator-prey systems are studied.All three predator-prey sys-tems have impulsive,Ivlev functional response functions.By analyzing the stability of the three predator-prey systems,sufficient conditions for the global stability of the system's persistence and extinction periodic solutions are obtained,and the correctness of some conclusions is verified by numerical simulation.In chapter one,this paper mainly introduces the research status and background of predator-prey system,impulsive and Ivlev type functional response and other functional response functions respectively,and finally introduces the preparatory knowledge needed in the research of this paper.In chapter two,the dynamic system of a predator-prey model with impulsive growth and functional response of Ivlev type is studied.The prey grows at impulsive time and continuously harvests the predator at non-impulsive time.The global asymptotic stability of predator extinction Period solution and sufficient conditions for the model to last are obtained by using impulsive differential equation comparison theorem,small amplitude perturbation and Floquet multiplier theory.Finally,the correctness of relevant conclusions is verified by numerical simulation in this chapter.In chapter three,the persistence and stability of a two predator-prey system with impulsive effect and functional response of Ivlev type are studied.In the system,two predators are put in a constant at the impulsive time.By using the comparison theorem of impulsive differential equations and the theory of Floquet multiplier,the global asymptotic stability of the extinction Period solution of the prey and the sufficient conditions for the persistence of the two predators-prey are proved.Finally,The correctness of the conclusion is verified by numerical simulation.The fourth chapter,in the first two chapters of this paper,we study the model with two preys and the competitive re.lationship between the two preys.We divide the predator into adult and juvenile.Considering spraying pesticides on one of the preys at impulsive time,we put a constant on the predator and obtain the local asymptotic stability of the periodic solution of the extinction of the prey and the final permanent filling of the model through the comparison theorem of impulsive differential equations.The validity of the persistence conclusion is proved by numerical simulation with matlab under different conditions.