Computer simulation of two chemostat models for one nutrient resource

We consider Michaelis-Menten chemostat dynamic models, describing the process of continuous cultivation of bacteria with one organic substrate and two types of microorganisms in a case where the Michaelis-Menten constants for the two competing species of microorganisms are equal. For such a system we obtain solutions with the finite initial conditions assuming only positive values. As it is shown the problem is reduced to the solution of the nonlinear differential equation of the first order. For some parametric relations the solutions of the differential system are found in the analytical form. Using numerical procedures we construct software modules that allow modeling the chemostat cultivation for the changing parameters and visualizing the dynamics of the development process for each microorganism. A comparative analysis of some numerical methods that are used to integrate the resulting nonlinear differential equation is given.