Electron. J. Differential Equations, Vol. 2017 (2017), No. 255, pp. 1-13.

Mathematical modelling and analysis for a three-tiered microbial food web in a chemostat

Miled El hajji, Nejmeddine Chorfi, Mohamed Jleli

Abstract:
In this article, we present a mathematical six-dimensional dynamical system involving a three-tiered microbial food web without maintenance. We give a qualitative analysis of the model, and an analysis of the local stability of equilibrium points. Under general assumptions of monotonicity, we prove the uniqueness and the local stability of the positive equilibrium point corresponding to the persistence of the three bacteria. Possibilities of periodic orbits are not excluded and asymptotic coexistence is satisfied.

Submitted April 12, 2017. Published October 11, 2017.
Math Subject Classifications: 35N25, 49K40.
Key Words: Mathematical modelling; three-tiered microbial food web; local stability; coexistence; Anaerobic digestion.

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Miled El Hajji
General studies department
College of Telecom and Electronics
Technical and Vocational Training Corporation
Jeddah 2146, Saudi Arabia
email: miled.elhajji@enit.rnu.tn
Nejmeddine Chorfi
Department of Mathematics
College of Sciences
King Saud University
Riyadh 11451, Saudi Arabia
email: nchorfi@ksu.edu.sa
Mohamed Jleli
Department of Mathematics
College of Sciences
King Saud University
Riyadh 11451, Saudi Arabia
email: jleli@ksu.edu.sa

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