The attractiveness of the Droop equations. II. Generic uptake and growth functions.

In a recent paper the authors proved global asymptotic stability of the Droop equations. This system of nonlinear ordinary differential equations describes the growth of a microorganism in a chemostat. In this setting the growth rate of the organism is limited by the availability of a single nutrient. The state variables of the Droop system are biomass density, intracellular nutrient concentration. (I"cell quota" in Droop's terminology), and extracellular nutrient concentration. In the current paper the authors relax Droop's particular choices for the uptake and growth functions. Characterizing these functions in qualitative terms only, they again reach the same conclusion of global asymptotic stability. Their analysis relies on reducing the three-dimensional Droop system to a two-dimensional system via the first integral of Burmaster.