Stability of Equilibria in a Biofilm Reactor Model with Wall Attachment and Thermodynamic Growth Inhibition

Abstract

The dynamics of a mathematical model for a chemostat-type reactor is investigated. The model describes the temporal evolution of suspended and wall-attached bacterial populations, with the latter represented as a one-dimensional biofilm, subject to a non-reproducing growth-limiting substrate and a reaction product formed through bacterial utilization of the substrate. In particular, it is shown that, in the regime where the trivial (washout) equilibrium is unstable, there exists a unique nontrivial equilibrium that is locally asymptotically stable. Under slightly stronger assumptions, uniform persistence and global asymptotic stability of the nontrivial equilibrium are established.