Classification of static behavior of a class of unstructured models of continuous bioprocesses

The stability characteristics of a class of unstructured models of continuo us bioreactors are analyzed using elementary concepts of singularity theory and continuation techniques. The class consists of models for which the no n-biomass product formation rate is linearly proportional to the utilizatio n rate of limiting substrate. The kinetics expressions of cell growth and p roduct synthesis are allowed to assume general forms of substrate and produ ct. Global analytical conditions are derived that allow the construction of a practical picture in the multidimensional parameter space delineating th e different static behavior these models can predict, including unique stea dy states, coexistence of non-trivial steady states with wash-out condition s, and multistability resulting from hysteresis. These general results are applied to specific examples of bioprocesses and allow the study of the eff ect of kinetic and operating parameters on the stability characteristics of these models.