Survival Analysis Of A Stochastic Three-species Ecosystem With Markov Switching In Polluted Environments

The high speed development of social economy has brought great convenience to people's production and life,meanwhile,environmental pollution has become increasingly severe.Environmental pollution will change the function and structure of the environmental system and have an adverse effect on the survival of the population.Therefore,studying the population survival and change law in the polluted environment has become a hot issue in scientific research.While the population fluctuations will be affected by stochastic disturbances and the population cannot survive alone in the real world,it is vital to explore stochastic multi-population model in the polluted environment.There are two main types of noises: white noise and colored noise,where white noise is expressed as a derivative of Brownian motion,and colored noise is represented as a continuous time Markov chain.In this paper,we establish a stochastic three-species ecosystem with intrinsic rate of increase perturbed by white noise and Markov switching for all parameters.For stochastic cooperative three populations model,stochastic competitive three populations model,a model consisting of two competitive preys and one predator and a model involving two competitive predators and one prey,we obtain the sufficient conditions of stochastic extinction,stochastic non-persistence in the mean,stochastic weak persistence in the mean and stochastic strong persistence in the mean for each population by the theory of stochastic differential equations.We verified theorems by numerical simulation and given its ecological significance.Chapter 6 discussed the stochastic permanence of a stochastic three-species ecosystem with intrinsic rate of increase perturbed by white noise and Markov switching for all parameters.We also examine the results by numerical simulation.