ON THE STABILITY OF PERIODIC SOLUTIONS FOR A PRODUCT INHIBITION MODEL OF CONTINUOUS BIOLOGICAL REACTORS

Abstract

A three-variable product-inhibition model of a continuous fermentation process is considered. It is shown that as time progresses all solution trajectories in the three-dimension solution space approach a plane and thus the three-variable system is equivalent to a model involving only two variables. With this result, we are able to obtain the stability condition for limit cycles bifurcating from a non-washout steady state of the three-variable model, and at the same time rule out the possibility of developing chaotic trajectories through subsequent bifurcations.