Global Dynamics of a Model for Anaerobic Wastewater Treatment Process

Abstract

Anaerobic wastewater treatment process is a process where microorganisms including hydrolytic, acidogenic, acetogenic, and methanogenic bacteria degrade organic substance into biogas in an oxygen-free environment. The anaerobic wastewater treatment plant is still rare at the industrial scale because it is unstable under certain circumstances. We present a generalized differential equation model with n microbial species feeding on n types of substrates. We establish a procedure which enables us to decouple a pair of equations in each step, such that using the Bendixson–Dulac criterion and the Poincaré–Bendixson theorem, we can determine the globally attractive equilibrium of those two equations, depending on the parameter values. The procedure yields a sequence of threshold parameters which completely describe the global dynamics of the 2n-dimensional system. We show numerical simulations to support the theoretical results.