Qualitative Analysis Of Two Stochastic Mutualism Population Models

It is great significance to study the dynamic behavior of the stochastic mutualism population.This paper is divided into three chapters and mainly discusses the properties of the solutions of two kinds of mutualism population models with random perturbations.Chapter 1 mainly describes the domestic and foreign research trends of stochastic population model with noise interference,and gives the basic idea and research method of the model.Chapter 2 concerns a stochastic mutualism population model with two-parameter perturbation(?)Firstly,by constructing an appropriate Lyapunov function and using It(?) formula,the existence and uniqueness of global positive solutions of the model are proved.Secondly,according to Lyapunov function and exponential martingale inequality,the sufficient conditions for the ultimate boundedness and extinction of the two populations are given.Finally,the rationality of the results is verified by numerical simulation.Chapter 3 studies the following stochastic mutualism population model with L(?)vy jumpBy constructing an appropriate Lyapunov function,the existence and uniqueness of global positive solutions of the model are proved.Using It(?) formula and Lyapunov function method,sufficient conditions for the ultimate boundedness and extinction of two populations are given.When the model does not consider the influence of L(?)vy jumps,the results are consistent with the corresponding results in the existing literature.Thus,the results of existing literature are generalized.Finally,the rationality of the results is verified by numerical simulation.Finally,we summarizes the results obtained in the first two chapters,and some ideas for the follow-up work are given according to the research trends in recent years.