The Threshold Analysis For Stochastic Three Species In A Polluted Environment

The development of science and technology has accelerated the progress of industrialization,and brought great convenience to mankind.However,the question of environmental pollution has been more and more serious.And it has been a threat to the survival of the exposed populations.In addition,the population must closely related to the surrounding biological who survive in the nature.The relationship between various species of biological communities,usually around the substance,energy,information and habitat,etc.The interaction between the two populations,who survive in a common natural environment,include mutual coexistence,mutual competition,predator and prey,parasite and host.The interaction between three or general more interacting species is more complex than two groups.In this paper,we study stochastic cooperation,competitive,two-predator one-prey model model and one-predator two-prey model of three species in a polluted environment.And by studying the ecological model of each relationship,then,sufficient conditions for stochastic extinction,stochastic non-persistence in the mean and stochastic weak persistence in the mean for each population are obtained.The threshold between weak persistence in the mean and extinction for each population is derived.More over,we use the Milstein method to numerically simulate the solution.