Researches On Dynamics In Three Prdator-prey Systems With Refuge And Impulsive Control

In this paper,I mainly studied dynamics in three predator-prey systems with refuge and impulsive control theoretically and numerically,and then some better results are obtained.In Chapter 1,the research background of impulsive control dynamic system and prey refuge are introduced,and then its progress is stated.What’s more,a series of basic concepts and important lemmas are given.In Chapter 2,a predator-prey ecosystem with prey refuge and impulsive control is proposed first,and then the corresponding dynamics are studied.Especially,it is discussed how the critical factors influence dynamics in this system.Based on impulsive differential equation theory,the existence and stability of semi-trivial periodic solution is analyzed,and then the conditions with respect to population permanence are derived.Furthermore,some numerical simulations are carried out,by which the effects of critical factors,such as released amount and control period,on predator-prey dynamics are studied.The results from numerical simulation are agreement with analytical results very well.In Chapter 3,a predator-prey ecosystem with double impulsive control is presented based on the system in chapter 2,where the harvest of both prey and predator and release of predator are considered.The existence and globally asymptotical stability of the semi-trivial periodic solution are analyzed theoretically,and the threshold conditions for the permanence of biological population are obtained.Meanwhile,the numerical results are consistent with theoretical analysis.In Chapter 4,a predator-prey ecosystem with stage structure and prey refuge,which is described by a couple of impulsive differential equations with delay,is proposed based on the system in chapter 2.According to the theory of impulsive differential equation with delay,the globally asymptotical stability of semi-trivial periodic solution and the critical condition of system permanence are researched.Theoretical analysis and simulation results reveal that stage structure,prey refuge and delay have significant effects on the dynamics of population growth.