Qualitative Study Of Several Biomathematical Models With Random Disturbance

In recent years,stochastic differential equation has become a hot field in mathematics,which has attracted many scholars to participate in the research.Stochastic differential equations have important applications in many fields,such as economics,physics,biology,etc.This paper mainly discusses the application of stochastic differential equations in biological models.Based on studies from previous related work,since deterministic models are not able to explain biological phenomena well,this paper optimizes the model and establishes three biological models with random perturbation,then the properties of the stochastic model are studied by mathematical methods.Finally,the accuracy of the relevant conclusions is verified by numerical simulation using MATLAB.The main contents of the paper are as follows:1.This paper studies a kind of population competition model with random perturbation.First,the paper studies the stochastic asymptotic stability of the zero solution of the model by constructing the Lyapunov function.Then studies the ergodicity of the model,and gives the sufficient conditions for the existence of the stationary distribution of the model.Finally,the paper discusses the persistence and final extinction conditions of the two species through classification discussion.2.This paper studies a class of stochastic predator-prey model with functional response function.First,it proves the global existence and uniqueness of the solution of the model.Then,the paper discusses the long-term properties of the solution of the model,mainly including the conditions for the existence of the system’s stationary distribution and the long-term progressive properties of the solution.Finally,the paper gives the extinction conditions of pests using two different methods.3.This paper studies the dynamic behavior of a kind of stochastic SEIR model with saturation incidence.First studies the asymptotic behavior of the solution of the stochastic model near the disease-free equilibrium point of its corresponding deterministic system,and then the paper discusses the conditions of stochastic persistence and final extinction of the disease by constructing auxiliary functions.Finally,the article studies the existence conditions of the stationary distribution of the model by constructing appropriate Lyapunov functions.