| In recent years,stochastic differential equations have developed rapidly,especially in the field of biomathematics.This paper constructs a class of non-autonomous time-delayed rate-dependent predator-prey model.By using the Milstein method,L’Hopital’s rule,and Ito formula,the non-autonomous ratio-dependent predator-prey model is studied,sufficient conditions for persistence or extinction are achieved,Verify its conclusion through numerical simulation.Based on this,a kind of food chain model with time-delay-dependent dependence was constructed,and the behavior of the system solution was studied.The first chapter is the introduction of this article,which mainly introduces the research background and significance of the thesis,and the research status of stochastic differential equations and stochastic delay differential equations in the field of biomathematics.The second chapter mainly introduces the theoretical knowledge needed in this paper.Then,based on the foregoing,a class of food chain model with time-delay-dependent dependence was constructed,and the system solution was obtained.The second chapter mainly introduces the theoretical knowledge needed in this thesis.Chapter 3 mainly covers this content.Persistence and extinction of a stochastic non-autonomous ratio-dependent predator-prey model with delay is proposed and studied.Our results show that there exists a unique positive solution to the system for any positive initial value.Moreover,sufficient conditions for extinction,non-persistence in the mean and weak persistence are established under some simple assumptions.Finally,numerical simulations are illustrated to confirm our main results by the Milstein method.Chapter 4 is mainly based on Chapter 3,Consider introducing multiple groups for research,and establishes a kind of food chain model with time-delay ratio dependence,and finds the solution of the system.The final chapter summarizes the thesis,reflects on the shortcomings,and gives a prospect for future research in related fields. |
