The Asymptotic Behavior Of Stochastic Food Chain Model With Poisson Jumps

Population dynamics is a science that studies the interaction between population and environment and different populations.Mathematical models constructed on the basis of population dynamics can be used to describe,predict population trends,and guide the development process of populations,so as to better develop resources,make rational use of resources and protect the environment.However,various random disturbances in nature are everywhere.Therefore,compared with the deterministic model,considering the stochastic differential equation model to describe the population dynamics behavior can accurately describe the population trend.In this paper,we mainly analyze and study the dynamics of a stochastic three-species food chain model driven by the Brownian motion and the Poisson jumps,mainly including the following two aspects:In the first part,the survival of a stochastic three species food chain model with Pois-son jumps are analyzed in the paper,which includes existence and uniqueness of global positive solution as well as permanence in the mean of the highest species.Situations that some species are extinct and others are persistent in the mean are also clarified.The results show Poisson jumps can obviously change the survival of population,which can make the persistent population become extinct,or vice versa.Finally,the results are verified by numerical simulations.In the second part,the dynamics behavior of the stochastic three species food chain model with Poisson jumps is further studied.Some asymptotic properties of the model solution and the sufficient conditions for the global stability in the mean of each species are obtained.The correctness of the conclusion is verified by numerical simulation.