On the existence of sustained oscillations in a class of bioreactors

In this paper, the problem of rigorously characterizing the existence of limit cycles in a class of two-state bioreactors is addressed. The reactor class is the simplest one which retains the essences of the oscillatory phenomena, and ample enough to include a diversity of monotonic and nonmonotonic kinetics. On the basis of global dynamics framework, analytic conditions for the existence of limit cycles are drawn, and the results are applied to characterize the reactor behavior with a linear P controller. The results are physically interpreted and put in perspective with previous open and closed-loop bioreactor studies. The findings are illustrated with a representative case example though numerical simulations.