Bounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kinetics

Abstract

Dedicated to the memory of María José Garrido Atienza.This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random fluctuations on the input flow, which are modeled by means of the well-known Ornstein-Uhlenbeck process, are considered to obtain a much more realistic model fitting in a better way the phenomena observed by practitioners in real devices. Once the existence and uniqueness of global positive solution has been proved, as well as the existence of deterministic absorbing and attracting sets, the random dynamics inside the attracting set is studied in detail to provide conditions under which persistence of species is ensured, the main goal pursued from the practical point of view. Finally, we support the theoretical results with several numerical simulations.Junta de Andalucía P12-FQM-1492Ministerio de Ciencia, Innovación y Universidades (MCIU). España PGC2018-096540-B-I00Junta de Andalucía (Consejería de Economía y Conocimiento) FEDER US-1254251Junta de Andalucía (Consejería de Economía y Conocimiento) P18-FR-450