Abstract
The rich dynamics exhibited by the different models studied in previous chapters were all uncovered when the chemostat was operated under time-invariant
conditions. In this chapter, we investigate the dynamic charcteristics of an unstructed model of the chemostat when it is periodically forced. The dynamics
of continuous bioreactors subject to periodic forcing of one or more bioreactor
feed conditions were studied both theoretically and experimentally by a number of authors [4, 194, 272, 273, 281, 306, 339]. These studies showed that
suitable periodic variations in one of the bioreactor inputs, e.g., dilution rate
and feed concentration can, in a number of cases, improve the time-average
performance of the continuous bioprocess vis-a´-vis its operation at a stable
nontrivial steady state. In the aforementioned studies, the periodic forcing
was carried out around a stable steady state, i.e., a point attractor for which
the periodic operation of the bioreactor can only yield periodic behavior. In
this chapter a different situation is examined for which the chosen center of
forcing is itself a stable limit cycle. The bioreactor model selected for this
investigation consists of the classical unstructured model for which the yield
coefficient is linearly proportional to the substrate. This model was studied
in Chapter 4 and was shown to predict oscillatory behavior for a wide range
of model kinetic and operating parameters. The objectives of this chapter are
twofold. The first objective is to examine the different nonlinear patterns that
arise in the bioreactor when the substrate feed concentration is periodically
varied around a limit cycle. The results of the investigation illustrate the interactions between the feed inputs, i.e., substrate feed concentration and the
nonlinearities of the bioreactor. These results also show the impredictibility of
the behavior of the bioreactor resulting from these parametric perturbations.
Dramatic changes can be expected in the nature of the emerging dynamic
behavior of the forced process [20].