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Research Article


ScienceAsia 20 (1994): 043-059 |doi: 10.2306/scienceasia1513-1874.1994.20.043

 

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

 

YONGWIMON LENBURY AND BORIBOON NOVAPRATEEP

ABSTRACT: The dynamic behavior of a model for the continuous culture subject to product inhibition is investigated theoretically in terms of multiplicity and stability of steady states and existence and stability character 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 state, 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 types of behavior are then illustrated by numerical computation of cells and product concentration trajectories.

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Department of Mathematics, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand.

Received Jan 15, 1994