Dynamic Analysis Of Two Kinds Of Predator-Prey Models With Neutral Delay And Stage Structure Respectively

Population dynamics model is a kind of mathematical model that describes the dynamic relationship between population and environment,as well as population and population.It is of great value and practical significance to study population stability and other properties by using mathematical models.It can be applied to environmental science,energy development,disaster ecology,and also to predict,regulate and control the development process and trend of species.In this paper,two kinds of predator-prey models are analyzed.Firstly,we study a kind of Leslie predator-prey model with neutral delay,prove the existence of periodic solution of the model,and obtain sufficient conditions for the persistence and extinction of stochastic system.Secondly,a stochastic predator-prey model with stage structure and internal competition is studied,and the asymptotics,persistence and extinction conditions of the system are discussed.In the first chapter,the background and current situation of neutral predator-prey model and stochastic stage structure model are introduced.Then some preliminary knowledge are given.In the second chapter,we put forward a class of ratio-dependent Leslie predator-prey models.Firstly,the impulsive control is introduced into the neutral predator-prey model with time delay,and the existence of positive periodic solution is proved by using the coincidence degree theory.Secondly,a stochastic interference Leslie model "with Smith growth is established when the white noise interference is considered and the time delay is not considered.Applying Ito formula,we get the conditions of system persistence and extinction.Finally we verify the correctness of theoretical analysis with numerical simulations.In the third chapter,we construct a stochastic predator-prey model with age structure and mutual interference.For the corresponding deterministic model,we discuss the existence and local asymptotic stability of positive equilibrium points.For stochastic models,the existence and uniqueness of global positive solutions are proved by constructing appropriate Lyapunov functions.The asymptotic behavior of the system is discussed by using the Ito formula and inequality technique.Finally,by using the comparison theorem of stochastic differential equations and the law of large numbers,the conditions of mean persistence and extinction are obtained.In the fourth chapter,the work of the full text is summarized and forecasted.