Asymptotic Properties Of Two Stochastic Three-species Predator-prey Models

In the ecological system,the relationship between predator and prey has always existed,and the in-depth study of them is of great importance to the protection of the ecological environment.In order to study the effect of the noise perturbation for predator-prey model,the researchers introduce the external random perturbation into the deterministic differential equation.It is important to study the population model with noise perturbation for the development of biological population,and the conclusion is more realistic and more researchable.In this paper,the asymptotic properties of two stochastic three-species predator-prey models with white noise perturbation will be studied.The main results are listed as follows:For the first nonlinear stochastic model with white noise perturbation,the appropriate Lyapunov function is selected.By using Chebyshev inequality,It?'s formula and other theoretical knowledge,the properties of the model solution including globally unique solution and stochastically ultimate boundness have been studied.And under some conditions,the solution is stochastic permanence.Under different conditions,the permanence of the model solution is studied,and it is concluded that the stochastic population model is similar to the corresponding deterministic model.For the second stochastic model with white noise perturbation,based on Chebyshev inequality and It?'s formula,the appropriate Lyapunov function is selected,and the globally unique solution of the stochastic model has been studied.Under some conditions,by using the Hesse matrix,the globally asymptotic stability of the positive equilibrium solution for the second stochastic three-species predator-prey model is proved.In order to verify the validity of the conclusion,this paper gives some corresponding numerical simulations.