Dynamical Properties Of Several Stochastic Population Models

The single-species model and the two-species model are of great biological significance,so they have always been a key research topic in biomathematics.Lots of scholars have carried out research in this field and achieved outstanding results.In nature,biological populations will be affected by environmental noise,it is necessary for us to introduce the environmental noise into the deterministic models,and then we study the dynamical analysis of environmental noise on the system with the help of stochastic differential equation theory.In Chapter 3,we discuss the existence and uniqueness of the solution,the stationary distribution and ergodicity,strong stochastic persistence and asymptotic stability of the single-species models.The existence and uniqueness of the model solution is proved,as well use of the Lyapunov function and application the It(?) formula to study the stationary distribution and ergodicity of the model.To prove the strong stochastic persistence of the model,we utilize the method of asymptotic approximation of the linear model coefficients with the nonlinear model coefficients.In Chapter 4,the existence and uniqueness of the solution,stationary distribution and ergodicity,asymptotic stability of the solutions of the two group models with B-D functional functions are researched.The existence and uniqueness of the model solution is proved,we build the Lyapunov function and apply the It(?) formula to study the stationary distribution and ergodicity of the model.And we use appropriate inequality transformation techniques,construct suitable Lyapunov function and apply the It(?)formula and other theories and methods to study the asymptotic stability of the model.In this paper,we prove the existence and uniqueness of the solution,stationary distribution and ergodicity,asymptotic stability of the solutions of the four models.For each properties of the models,numerical simulations are used to support the validity of the theoretical results.