Analysis of a microfluidic chemostat model with random dilution ratios

In this paper, we first construct a microfluidic chemostat model for the growth of biofilms and planktonic populations with random dilution ratios and then investigate its dynamical behavior. Using the theory of monotone dynamical systems and the Multiplicative Ergodic Theorem, we show the existence of random attractors and stationary measures, and present Lyapunov exponents for the linearized cocycle with respect to the random model. Further on, if the top Lyapunov exponent is negative, we give the extinction of microbial populations, including the forward and pull-back trajectories.