Ergodic property of the chemostat: A stochastic model under regime switching and with general response function

The dynamics of chemostat involving stochastic perturbations is considered. Instead of assuming the familiar Monod kinetics for nutrient uptake, a general class of functions is used which includes all monotone (non-monotone) increasing uptake functions. We make two classifications of restrictive assumptions on the growth response. For the chemostat disturbed by both white noise and colored noise, we obtain the ergodic property by constructing stochastic Lyapunov function under small perturbation, which provide a good description of persistence. We observe that these assumptions on the functional response are relative weak and valid for many forms of growth response.