Periodic solution for the stochastic chemostat with general response function

This paper addresses a stochastic chemostat model with periodic dilution rate and general class of response functions. The general functional response is assumed to satisfy two classifications of conditions, and these assumptions on the functional response are relative weak that are valid for many forms of growth response. For the chemostat with periodic dilution rate, we derive the sufficient criteria for the existence of the stochastic nontrivial positive periodic solution, by utilizing Khasminskii's theory on periodic Markov process.