考虑一类具有变消耗率的随机恒化器模型.首先证明了随机模型具有全局唯一正解.利用随机Lyapunov 函数和伊藤公式,得到微生物灭绝和持久的充分条件,而且讨论了随机模型平稳分布的存在性.最后,通过数值模拟验证了变消耗率对微生物生长的影响.

In this paper, a stochastic differential equations chemostat model with variable yield and linear growth rate is formulated and studied. First, using the stop time and the inverse method, we verify that there is a unique global positive solution of the stochastic system. Second, by constructing appropriate stochastic Lyapunov functions and using It\^o formula, we find that the sufficient conditions of the extinction and persistence of the microorganism. In addition, the existence on the stationary distribution of the stochastic system is studied in detail. Finally, computer simulations are carried out to illustrate the obtained results and the effect of variable yield on the microorganism.