Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources

A model of the chemostat involving two populations of microorganisms competing for two complementary, growth-limiting substrates is considered. Instead of assuming the familiar Michaelis-Menten kinetics for nutrient uptake, a general class of functions is used which includes all monotone increasing uptake functions, but which also allows uptake functions that describe inhibition by the substrate at high concentrations. Graphical techniques are developed to analyze the model. In the case of monotone kinetics the results are similar to those of Hsu, Cheng, and Hubbell [16], who study this problem assuming Michaelis-Menten kinetics. For monotone kinetics, all dynamics are trivial in the sense that all solutions approach equilibria. However, when at least one of the competitors is inhibited by high concentrations of the substrate, one can easily construct examples for which there is a stable periodic solution. Surprisingly, if the substrates are inhibitory at high concentrations, there are examples for which coexistence is possible but neither competitor can survive in the absence of its rival.