中文摘要：

考虑了一类营养的输入浓度和稀释率同时受到白噪声干扰的随机恒化器模型.首先证明了模型正解的全局存在唯一性;其次通过构造Lyapunov函数的方法研究了在不同条件下随机模型的解围绕其相应确定性系统的正平衡点和绝灭平衡点的振荡行为;最后通过数值仿真验证了所得结论的正确性.

英文摘要：

A stochastic chemostat model was considered,in which both the input concentration ofnutrient and the dilution rote are simultaneously influenced by white noises,The uniqueness andglobal existence of the positive solution of the model were proved,and it was investigated how thesolution is oscillating around the positive equilibrium and the extinction equilibrium of thecorresponding deterministic model under different conditions.Numerical simulations were carriedout to illustrate the conclusions.