The Qualitative Analysis And Optimal Economic Benefit Of The Predator-prey Models

This paper mainly investigates two kinds of predator-prey systems,and one is multi-state dependent impulsive predator-prey system,the other is state-dependent impulsive predator-prey system with two types of harvesting.In order to determine the frequency of the impulsive coefficient,we investigate the existence and uniqueness of order-1 periodic solution by using the successor function method.Then,to ensure a certain robustness of adopted control,we prove the stability of periodic solutions is by using the analogue of the Poincare criterion.Furthermore,we present the optimization strategy for obtaining the maximum economic benefit,and obtain the optimal threshold.This paper includes four sections as follows.In Chapter 1,we mainly introduce the research background and the concept and application of the semi-continuous dynamic system.In Chapter 2,we propose a predator-prey system with Holling type-I functional response and multi-state impulsive feedback control,where the parameters are linearly dependent on the threshold in the second impulse.Firstly,we investigate the existence of order-1 periodic solution of the system by using successor functions and Bendixson theorem of impulsive differential equations,then under certain conditions,we prove the stability of periodic solutions is proved by using the analogue of the Poincare criterion.Furthermore,in order to reduce the actual total cost and obtain the best economic benefit,the optimal economic threshold is obtained,which provides the optimal strategy for the practical application.Finally,we use the Maple numerical simulation to verify the feasibility of the theorem-related results.In Chapter 3,we propose a state-dependent impulsive predator-prey system with two types of harvesting in which the impulse parameters are linearly related to the threshold.By first using the differential equation geometry theory and successor function method,we discuss the existence,uniqueness and asymptotic stability of the periodic solution.And then numerical simulations illustrate the feasibility of the theoretical results.Then we use the Maple numerical simulation to verify the theoretical results.Moreover,in order to increase the total profit,we present the optimization strategy and obtain the optimal threshold.Finally,we use the Maple numerical simulation to verify the theoretical results.In Chapter 4,we make a summary and prospects.