Competition of two microbial species in a turbidostat

The competition between two microbial species in a chemostat definitely leads to the disappearance of one of them (Smith and Waltman, 1995). In this paper, a turbidostat is taken into account, i.e., a continuous bioreactor in which the microbial concentration is controlled by manipulating the feed rate, and the competition between two microbial species is modelled by means of Mathematica® and AUTO97 simulation codes. The growth of the two populations is supposed to be described by a simple unstructured model, the growth rate being a function of the limiting substrate concentration for both species. It is shown that there is a range of the set point parameters for which the continuous bioreactor has a steady state in which the microbial species can coexist. The stability of such solutions depends on both the growth rate and the microbial yield. If the growth kinetics are monotonic with substrate concentration (such as the Monod-like one), no periodic solutions can occur. On the contrary, if the growth rates are not monotonic, the bioreactor can show periodic regimes, too. Such regimes can involve either oscillations of the concentration of a single species (while the other is constantly equal to zero) or oscillations of the concentrations of both the populations.