污染环境中具有Markov切换的随机三种群竞争系统生存分析

Survival Analysis of Stochastic Competitive Three Populations with Markov Switching in Polluted Environments

本文研究污染环境下受到毒素和双重噪声(白噪声和有色噪声)作用的随机系统,建立污染环境中具有Markov切换的随机三种群竞争模型.一方面,本文得到系统中各种群灭绝、随机非平均持久的充分条件;另一方面,考虑到系统中竞争作用对种群生存状态产生的影响,本文得到系统中各种群随机弱平均持久及随机强平均持久的充分条件.文末也通过数值模拟显示出相应的理论结果.

In this paper, we study the stochastic system with the effects of toxin and double noise(white noise and colored noise) in the polluted environment, and establish a stochastic competitive three populations model with Markov switching. On the one hand, we obtain the sufficient conditions of extinction and stochastic non-persistence in the mean for each population;On the other hand, considering the effect of competition on the survival of the population in the system, we get the sufficient conditions of stochastic weak persistence in the mean and stochastic strong persistence in the mean for each population. And we present the corresponding theoretical results through numerical simulation.