Stability Analysis of a Chemostat Model for Phenol and Sodium Salicylate Mixture Biodegradation

Abstract

In this paper we consider a mathematical continuous-time model for biodegradation of phenol in the presence of sodium salicylate in a chemostat. The model is described by a system of three nonlinear ordinary differential equations. Based on the dynamical systems theory we provide mathematical investigations of the model including local and global analysis of the solutions. The local analysis consist in computation of two equilibrium points—one interior and one boundary (washout) equilibrium—in dependance of the dilution rate as a key model parameter. The local asymptotic stability of the equilibria is also presented. The global analysis of the model solutions comprises proving existence, uniqueness and uniform boundedness of positive solutions, as well as global asymptotic stabilizability of the dynamics. The theoretical investigations are illustrated by some numerical examples. The results in this study can be used in practice as a tool to control and optimize the chemostat performance of simultaneous biodegradation of mixed substrates in wastewater.