The operating diagram for a two-step anaerobic digestion model

The anaerobic digestion model ADM1 is a complex model which is widely accepted as a common platform for anaerobic process modeling and simulation. However, it has a large number of parameters and states that hinder its analytic study. Here, we consider the two-step simple model of anaerobic digestion named AM2, which is a four-dimensional system of ordinary differential equations. The AM2 model is able to adequately capture the main dynamical behavior of the full anaerobic digestion model ADM1 and has the advantage that a complete analysis for the existence and local stability of its steady states is available. We describe its operating diagram, which is the bifurcation diagram giving the behavior of the system with respect to the operating parameters, represented by the dilution rate and the input concentrations of the substrates. This diagram is very useful to understand the model from both the mathematical and biological points of view. It is shown that six types of behavior can be obtained for the long-term dynamics of the AM2 model, concerning the coexistence or extinction of one or both bacterial populations.