Oscillations in continuous cultures of microorganisms: criteria of utility of mathematical models

This article proposes a new approach to the modeling of continuous cultures of microorganisms based on the concept of universality classes. Instead of analysis of concrete sets of equations, vast classes including models with identical qualitative features should be studied. The class of models of the second order is the simplest one, and it is analyzed in order to demonstrate the mathematical methods used. The authors have shown that the simplest model usually used for the description of continuous cultures is sensitive to even slight modifications. The modified model changes its properties and gives rise to a class of models that are applicable to the description of damped and nondamped oscillations of biomass and substrate concentrations in a fermenter. Irrespective of the mode of the initial model modification, the oscillations have a number of common features. These features can be used as the criteria of utility of this class of models for simulation of culture behavior. Two models of the class in question (with nonzero maintenance coefficient and nonconstant yield) are analyzed using these criteria.