A stochastic chemostat model with periodic washout rate is first proposed.

We apply the Khasminskii’s theory on periodic Markov processes to investigate the periodic solutions.

A new Lyapunov function has been established to prove the existence of the nontrivial positive periodic solution and the global attractivity of the boundary periodic solution.

Converging the white noise σb>1b>(t  ) to zero, we can get the threshold quantity b=MathURL&_method=retrieve&_eid=1-s2.0-S1007570416000046&_mathId=si13.gif&_user=111111111&_pii=S1007570416000046&_rdoc=1&_issn=10075704&md5=72c0850d48b23288bffcad20289645ad"> which is expressed in terms of the system parameters and the intensity of the white noise.

The conditions for the existence of the periodic solutions are more general than that in pre-existing papers.