The Research On Dynamic Of Stochastic Three-species Systems In Polluted Environment

With the rapid development of the world economy,the living standards of human being have been greatly improved.Meanwhile,environmental pollution has become increasingly serious,which greatly threatens the security of ecosystems and the health of human.This situation determines whether the future economic and society is sustainable development or not.How to control the deterioration of the environment and make it conducive to the sustainable survival of future biological populations and humans has become a hotspot.Therefore,this paper mainly studies the stochastic three-species system in the polluted environment and analyzes its dynamic behavior.It is mainly divided into three parts:In the first part,based on a deterministic model of two prey and one predator with time delay in a polluted environment,taking the random factors and Lévy noise into the model,and obtain the thresholds for extinction and strong persistence in the mean.It is concluded that time delays are harmless to the persistence in time average and extinction of our model;Lévy noise and toxin concentration will seriously affect the survival of the population.In addition,we introduce some numerical simulations to illustrate the theoretical results.In the second part,a stochastic Leslie-Gower Holling-type II two-preys one-predator model with impulsive toxicant input in polluted environments is established.We use tsoI ?’formula to study the dynamic behavior of the model,obtain the thresholds for the extinction,stable in the mean and strongly persistence in the mean of the solution.Numerical simulations are used to further verify the rationality of the conclusions.In the third part,a stochastic tri-trophic food chain model in a polluted environment is proposed in this paper.We prove that the model has a globally unique global positive solution.Meanwhile,the thresholds of extinction and strongly persistence are given,Moreover,we demonstrate the stability in distribution of this model.We introduce some numerical simulations to illustrate the theoretical results.