A MATHEMATICAL MODEL OF THE WAY MICROORGANISMS REPRODUCE AT THE EXPENSE OF NUTRIENT CONSUMPTION IN THE CHEMOSTAT
One of the simplest experiments in microbiology is the growing unicellular microorganisms such as bacteria and following changes in their population over a period of time. We discuss the mathematical representation of such an experiment as modeled by  (for equations see 'Additional Files' below) where N(t) represents the density of the microorganism, C(t) is the concentration of the stock nutrient, C0 is the initial concentration, Kmax represents an upper bound for K(C), and for C = Kn, K(C) = (1/2)Kmax , µ is the mortality rate of the microorganism, while D and α are rate parameters. We use dimensional analysis to reduce the number of parameters and also calculate the steady states and investigate their linear stability properties.  G.F Gause, The Struggle for Existence. (Hafner Publishing, New York, 1969).
"A MATHEMATICAL MODEL OF THE WAY MICROORGANISMS REPRODUCE AT THE EXPENSE OF NUTRIENT CONSUMPTION IN THE CHEMOSTAT,"
Georgia Journal of Science, Vol. 75, No. 1, Article 79.
Available at: https://digitalcommons.gaacademy.org/gjs/vol75/iss1/79