| In this paper,I mainly investigate several prey-predator systems with impulsive control theoretically and numerically,and some important results are obtained.In chapter 1,the research background is desecibed firstly,and then some definitions and lemma are given.In chapter 2,a prey-predator system with Beddington-DeAngelis functional response and impulsive control is studied.The existence and stability of positive equilibrium is discussed,by which the existence and stability of semi-trivial periodic solution and order-1 periodic solution is analyzed.What's more,theoretical analysis shows that the semi-periodic solution can lose its stability via fold bifurcation,and then an order-1peridoc solution emerges.Finally,some numerical simulations are carried out,which are agreement with analytical results very well.In chapter 3,a prey-predator system with Crowley-Martin functional response and impulsive control is proposed firstly.Using of the impulsive differential equation theory,dynamics in this system is studied,including the existence of semi-trivial periodic and its stability,the existence and stability of order-1 periodic solution.According to these results,some numerical simulations are performed,which shows that chaos can occur.Obviously,impulsive control plays an important role in population growth dynamics.In chapter 4,the control depending on predator population is considered based on the system in chapter 3,and then the corresponding prey-predator system is presented,where dynamics in this system is discussed.By successor function and geometrical methods with respect to differential equation,the existence and stability of order-1 periodic solution are proved.Especially,there is no order-3 and others higher order periodic solutions under some conditions,which means that chaoscan not emerge corresponding to these conditions,and then it is possible that population density can predicted using models.In chapter 5,this paper ends with a summary and its discuss. |
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