Stability and bifurcation of an unstructured model of a bioreactor with cell recycle

An unstructured model of a bioreactor with cell recycle and substrate inhibition kinetics is used to investigate the bifurcation and stability characteristics of this unit. The singularity theory used for this investigation allows a global analysis of steady-states multiplicity and the different bifurcation mechanisms occurring in the system including hysteresis and pitchfork. Analytical criteria are also derived for the safe operation of the reactor and to prevent wash-out conditions. The investigation of the dynamic bifurcation, on the other hand, shows that the model cannot exhibit periodic attractors with any growth kinetics model. The inability of this widely used model to exhibit periodicity despite the experimental results that support the existence of periodic behavior in many bioreactors suggests that new approaches are to be taken for the modeling.