Non-Existence of Periodic Solutions in a Model of Continuous Fermentation

A general criterion is given for the absence of non-trivial periodic solutions in a model of continuous fermentation. In the model there is one species of micro-organism and one single limiting substrate. The model allows for uptake rates with substrate inhibition, variable yield coefficients, variable endogenous decay rates, separation of micro-organisms from the outflowing stream, and non-zero micro-organism feed rates. The criterion implies in particular the absence of non-trivial periodic solutions if the yield coefficient and the endogenous decay rate are constant.