Random and stochastic disturbances on the input flow in chemostat models with wall growth

Abstract

In this paper, we analyze a chemostat model with wall growth where the input flow is perturbed by two different stochastic processes: the well-known standard Wiener process, which leads into several draw- backs from the biological point of view, and a suitable Ornstein- Uhlenbeck process depending on some parameters which allow us to control the noise to be bounded inside some interval that can be fixed previously by practitioners. Thanks to this last approach, which has already proved to be very realistic when modeling other simplest chemostat models, it will be possible to prove the persistence and coexistence of the species in the model without needing the theory of random dynamical systems and pullback attractors needed when dealing with the Wiener process. This is an advantage since the theoretical framework in this paper is much less complicated and provides us much more information than the other.