Study Of Two Classes Of Single Population Models With Distributed Delay And Nonlinear Harvesting

Biomathematics is a hot subject,and many biomathematicians have conducted in-depth research and obtained many excellent results.In particular,in terms of biological populations,the results provide a good guide for biological resource management.In this thesis,we consider the effects of time delay,nonlinear harvesting and proper control of human on the survival and development of the population,using the knowledge of the ordinary differential equation geometry theory,ordinary differential equation bifurcation theory and impulsive differential equation geometry theory,the dynamics of two classes of single-population models with distributed time-delay and nonlinear harvesting are studied,and the correctness of conclusions is verified by numerical simulation.The thesis has three chapters,and the summarization is as followed:The first chapter introduces the research backgrounds,research significances and research status,and also outlines the main works that we have done in this thesis.In the second chapter,the single population model one with distributed time delay and nonlinear harvesting is studied.The sufficient conditions for the existences and stabilities of the equilibria and limit cycle of the model under different conditions are obtained.The sufficient conditions for the existences of Hopf bifurcation are also determined.The correctness of the results is verified by numerical simulation.In the third chapter,based on the model one,the state pulse feedback control is used to establish the single population model two with state impulse feedback control,distributed time delay and nonlinear harvesting.Based on some theoretical results in the second chapter,the existence and stability of the order-1 periodic solution of the model under the case that the model has only one positive equilibrium point are discussed.Finally,the main conclusions are verified by numerical simulation.