Operating diagrams for a three-tiered microbial food web in the chemostat

In this paper, we consider a three-tiered food web model in a chemostat, including chlorophenol, phenol, and hydrogen substrates and their degraders. The model takes into account the three substrate inflowing concentrations, as well as maintenance, that is, decay terms of the species. The operating diagrams give the asymptotic behavior of the model with respect to the four operating parameters, which are the dilution rate and the three inflowing concentrations of the substrates. These diagrams were obtained only numerically in the existing literature. Using the mathematical analysis of this model obtained in our previous studies, we construct the operating diagrams, by plotting the curves that separate their various regions. Hence, the regions of the operating diagrams are constructed analytically and there is no requirement for time-consuming algorithms to generate the plots, as in the numerical method. Moreover, our method reveals behaviors that have not been detected in the previous numerical studies. The growth functions are of Monod form with the inclusion of a product inhibition term. However, our method applies for a large class of growth functions. We construct operating diagrams with and without maintenance showing the role of maintenance on the stability of the system.