Analysis Of Two Types Leslie-Gower Model With State Feedback Control

The insect is the common name of insect which is harmful to human beings.The outbreak of pests will reduce the yield and quality of crops,which will affect the interests of farmers.Therefore,the effective pest control methods attract great attention.In practice,people put forward many pest control methods,such as biological control,physical control and chemical control and so on.In this paper,applying state dependent impulsive differential equation to describe and study the two types of state feedback control of Leslie-Gower predator-prey model.In the chapter one,the impact of the pest,control measures,mathematical research status and preliminaries are introduced.In the chapter two,a type of Leslie-Gower model with ratio-dependent functional response and integrated pest management is introduced and investigated.For the continuous system,the positivity and boundedness of the solution is analyzed,and the existence and global asymptotic stability of the positive equilibrium is discussed.By applying the successor function and Analogue of Poincar?e criterion,the existence and stability of the order-1 periodic solution is discussed.In addition,to minimize the total cost in the pest control process,an optimization problem is formulated and the optimum pest control level is obtained.At last,the existence of order-2 periodic solution and order-3periodic solution can be obtained by numerical simulation.In the chapter three,a type of Leslie-Gower model with alternative food for predator and state feedback control is introduced and investigated,where the yield of releases of predator and the strength of pesticide spraying are linearly dependent on selected control level.For the continuous system,the existence and stability of the positive equilibrium is analyzed.By applying the successor function,the existence of the order-1 periodic solution is discussed;by applying the Analogue of Poincar?e criterion,the sufficient condition of the stability of the order-1 periodic solution is obtained.Applying numerical simulations to verify the theoretical results,the theoretical and numerical results indicate that the integrated pest management could keep the pest below the economic injury level.