THEORETICAL INVESTIGATION OF A PRODUCT INHIBITION MODEL FOR A CONTINUOUS-CULTURE - EFFECT OF YIELD TERM AND PARABOLIC SPECIFIC GROWTH-RATE

The dynamic behavior of a model for the continuous culture subject to product inhibition is investigated theoretically in terms of multiplic ity and stability of steady states and existence and stability charact er of limit cycles. It is shown that bifurcation of periodic solution cannot occur from the washout steady state of the model system. At the point of bifurcation Of periodic solution from a nontrivial steady st ate, however, an increase in the substrate concentration must decrease the specific growth rate and increase the substrate consumption rate. Various boundary conditions are derived which delineate the parameter space into regions of dynamically different behavior. The predicted t ypes of behavior are then illustrated by numerical computation of cell s and product concentration trajectories.