Chemostat models with Monod and Haldane consumption functions and random environmental fluctuations

Abstract

In this paper, we study the asymptotic dynamics of two chemostat models with random environmental fluctuations modeled by means of real noise, where different consumption functions for the consumer species (Monod and Haldane) are taking into account. For each model, our main goal is to investigate the existence of deterministic attracting sets. This allows us to provide conditions under which the species become extinct or persist, which is the main goal in industrial setup. In addition, we depict different numerical simulations to support the theoretical results. Finally, we present some conclusions to sum up our contribution and we compare how the species behave depending on its consumption function.