Analysis of a mathematical model of syntrophic bacteria in a chemostat

TL;DR

This paper develops and analyzes a mathematical model describing the coexistence and stability of syntrophic bacteria in a chemostat, with implications for anaerobic digestion processes.

Contribution

It introduces a new mathematical model for syntrophic bacteria in a chemostat and provides a detailed stability analysis under general monotonicity assumptions.

Findings

Positive equilibrium is asymptotically stable under general conditions.

The model demonstrates coexistence of bacteria in stable equilibrium.

Applicable to real-world anaerobic digestion processes.

Abstract

A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out. The local and global stability analysis of the equilibria are performed. We demonstrate, under general assumptions of monotonicity, relevant from an applied point of view, the asymptotic stability of the positive equilibrium point which corresponds to the coexistence of the two bacteria. A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model.