Survey on chemostat models with bounded random input flow

Abstract

In this paper we study some chemostat models with random bounded fluctuations on the input flow. We start with the classical chemostat system and obtain new models incorporating, for instance, wall growth and different consumption functions, motivated by phenomena in real devices. In every case, we prove existence and uniqueness of positive global solution, existence of deterministic absorbing and attracting sets and we investigate the internal structure of the attracting sets to obtain detailed information about the long-time dynamics of the systems. This allows us to provide conditions under which either extinction or persistence of the species is ensured, the main goal for practitioners. In addition, we provide several numerical simulations to support the theoretical results.

Keywords

• chemostat
• bounded noise
• ornstein-uhlenbeck
• wall growth
• non-monotonic consumption function