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In this paper, we get the analogue which is identified as the break-even concentration of the stochastic chemostat mode. If the analogue is bigger than the input concentration of the nutrient, the microorganism is extinct in the chemostat; if the analogue is less than the input concentration of the nutrient, the microorganism is persistent in the chemostat. If the noise of microorganism is big enough, the microorganism is always extinct irrespectively the noise.