A MATHEMATICAL MODEL OF TWO COMPETING SPECIES IN A SIMPLE CHEMOSTAT WHEN THE GROWTH FUNCTION OF EACH SPECIES IS OF CONTINUED FRACTION FORM

A chemostat is laboratory device used in ecological studies of microorganisms. A simple mathematical model for two microorganisms competing for the same limiting resource in a chemostat is considered. The model consists of three ordinary differential equations of nonlinear type. The system has four parameters: The washout rate, the input concentration, the maximum growth rate and the half saturation rate. It had been shown that coexistence is not possible when these parameters are constant and when the growth functions are of Michaelis-Menten form or other monotone forms. In this work, we studied a modified chemostat model when the growth and consumption functions of each species are allowed to be of continued fraction form. We used the mathematical software PHASER to study the chemostat model under these modifications. The study has shown that coexistence is not possible under the new modifications.