AM2 model with a series configuration of interconnected chemostats and distinct removal rates

TL;DR

This paper analyzes the complex dynamics of a two-chemostat interconnected system with distinct dilution rates, characterizing all steady states and stability conditions, and highlighting the potential for oscillations and bifurcations.

Contribution

It provides a comprehensive qualitative analysis of the AM2 model with interconnected chemostats, including stability conditions and bifurcation insights, for the first time.

Findings

Characterized all steady states and their stability conditions.

Identified conditions for coexistence equilibria and their stability.

Highlighted open problems related to oscillatory behaviors and bifurcations.

Abstract

We investigate the dynamics of the AM2 model in a serial configuration of two interconnected chemostats with distinct dilution rates. The system is described by nonlinear differential equations, for which the usual reduction from an eight-dimensional system to a four-dimensional one is no longer possible due to the distinct dilution rates. We provide a complete qualitative study by characterizing all steady states and establishing necessary and sufficient conditions for the existence, multiplicity, and local stability of nine types of equilibria, expressed in terms of key operating parameters. We show that coexistence equilibria involving two species in the second bioreactor are not always stable, even when they exist, and require an additional condition related to the trace of the Jacobian matrix. Identifying parameter sets leading to Hopf bifurcations and limit cycles remains an open problem. These results provide new insights into the dynamics of interconnected bioreactors and motivate further investigations on oscillatory behaviors.