Dynamic Analysis Of A Stochastic Non-autonomous Predator-prey System With Crowley-Martin Type Functional Response

The predator-prey system with functional response has been played an impor-tant role in the population dynamics.Recently,the predator-prey system with Crowley-Martin functional response has attracted the attention of many experts abroad.However,the random disturbance factor was neglected in the tradition-al system.In this paper,we study the dynamics of a stochastic nonautonomous predator-prey system with Crowley-Martin functional response.Firstly,the research background and practical significant of the system are briefly introduced.Then,the existence of a global positive solution and stochas-tically ultimate boundedness are derived based on the biological significance of the system.After that the paper discusses the persistence and extinction of the model.By using Ito formula and constructing appropriate Lyapunov functions,sufficien-t conditions for extinction?non-persistence in the mean?weak persistence in the mean and strong persistence in the mean of prey population are established,and sufficient conditions for extinction?non-persistence in the mean and weak persis-tence in the mean of predator population are also established.Next,we perform numerical simulations by using Milstein method to show our analytical findings.Fi-nally,The global attractiveness of the solution is also considered and the sufficient criterion for global attractiveness of the solution is derived.Lastly,the numerical simulations are carried out to support our findings.