Study Of Two Classes Of Single Population Models With Distributed Delay And Holling Type ? Response Function

Biomathematics is the intersection of biology and mathematics,whose role is to allow us to discover mathematical phenomena in biology and solve the mathematical problems in biology.In recent years,biological mathematical models have attracted more and more scholars' attention.In the paper,a class of single-population model with distributed time-delay and Holling type ? response function is studied,we use the qualitative knowledge of ordinary differential equations and the theory of bifurcation to analyze the dynamic behavior of the system.And then we add impulse feedback control to the previous model,a class of single-population model with distributed delay and impulse feedback control and Holling type ? response function is established.The periodic solution of the model is analyzed by using the knowledge of the geometric theory of impulse differential equations.Finally,the correctness of the conclusion is verified by numerical simulation.The paper includes three chapters,the basic content is as follows:The first chapter introduces the research backgrounds,research significances and research status,and briefly summarizes the main content of the paper.In chapter 2,by considering time delay and nonlinear harvesting,we establish a class of single-population model with distributed time-delay and Holling type ? response function.Through the discussion of the existence and stability of the positive equilibrium points,sufficient conditions for locally or global stability of positive equilibrium points are obtained.Hopf bifurcation with parameter ? is studied by using bifurcation theorem,and the conclusion is verified by numerical simulation.In chapter 3,a single population model with distributed time-delay and impulse feedback control and Holling type ? response function is established on the basis of chapter 2.Based on the contents of chapter 2,the existence and stability of the order-1 periodic solution of the model with only one positive equilibrium point are discussed.Finally,the correctness of the inference is verified by numerical simulation.