Hopf bifurcations of a variable yield chemostat model with inhibitory exponential substrate uptake

In this paper, we consider a simple chemostat model involving a single species feeding on redundant substrate with a variable yield term. Many experiments indicate that very high substrate concentrations actually inhibit growth. Instead of assuming the prevalent Monod kinetics for growth rate of cells, we use a non-monotonic functional response function to describe the inhibitory effect. The existence of periodic solutions when certain parameters of the model assuming a specific ratio is shown.