Non-autonomous chemostat models with non-monotonic growth

Abstract

In this paper, we investigate four non-autonomous chemostat models with non-monotonic consumption function, where wall growth and nutrient recycling are also taken into account. In each case, we prove the existence and uniqueness of non-negative global solution that generates a non-autonomous dynamical system. In addition, we also prove the existence of a unique (global) pullback attractor whose internal structure provides detailed information about the long-time behaviour of the state variables, for instance, conditions to ensure the extinction and the persistence of the species. We also display numerical simulations to illustrate the theoretical results.

KEYWORDS:

• Chemostat model
• non-monotonic growth
• wall growth
• pullback attractor
• persistence

AMS SUBJECT CLASSIFICATIONS:

• 92D25
• 34C60
• 34D23
• 92D30

Acknowledgements

These authors would like to thank the anonymous referees, whose reports helped us to improve the earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research has been partially supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) under the project PGC2018-096540-I00, and by Junta de Andalucía and FEDER under the projects US1254251 and P18-FR-4509. The third author has also been funded by Programa Operativo de Empleo Juvenil 2014-2020 from Junta de Andalucía.