Modeling and Analyzing the Long-Time Behavior of Random Chemostat Models

In this work, the simplest chemostat model, perturbing the input flow by means of the Ornstein-Uhlenbeck process, will be presented. We will make use of the techniques involved in the theory of random dynamical systems to provide some results concerning the existence and uniqueness of global solution just like the existence and uniqueness of random pullback attractor, which will allow us to obtain detailed information about the long-time behavior of our model. In particular, some conditions on the different parameters of our model will be given to ensure the persistence of the microbial biomass. Finally, several numerical simulations comparing the results with the ones obtained when perturbing the input flow by using the standard Wiener process will be also shown