污染环境中具有Markov切换的随机互惠三种群生存分析

摘要

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切换的随机互惠三种群模型.利用随机微分方程相关理论和分析方法, 考虑系统同时受到白噪声、有色噪声、毒素浓度及种群间相互作用因素对种群生存状态的影响, 得到随机互惠三种群系统中各种群趋于灭绝、随机非平均持久、随机弱平均持久和随机强平均持久的充分条件.数值模拟验证了理论结果的正确性.%Consider the stochastic system with the effects of toxin and double noise (white noise and colored noise) in the polluted environment, and establish a stochastic cooperative three populations model with Markov switching. Taking white noise, colored noise, toxin concentration and the interaction between populations into account, 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 are obtained by the theory of stochastic differential equations and related analysis method. The correctness of theoretical results is tested through numerical simulation.