A Basic Chemostat -- Non-Dimensional Form by Mike Martin

On this page, plots of solutions for a simple chemostat model that has been non-dimensionalized (variable transformations are utilized so that the number of parameters can be minimized). In particular, the original basic chemostat model can be found at the following link. The original equations for the basic chemostat model are:

The equations for this new system are:

Plots of the non-dimensionalized bacteria and nutrient concentrations are given below and the phase portrait with stream lines is below the concentration plots. The user inputs values of the parameters m and α. Also, gird bounds, time bounds, and the initial conditions must be specified.

Enter in the value of the parameters and select the plotting bounds, then press the "Plot/Evaluate" button.

m_{} =

α =

S (0) =

x (0) =

0 ≤ t ≤

≤ x ≤

≤ S ≤

References:

Wikipedia's Phase Portrait MathWorld's Phase Portrait DFIELD & PPLANE -- web utilities Community of Ordinary Differential Equations Educators

MathWorld's Phase Portrait

DFIELD & PPLANE -- web utilities

Community of Ordinary Differential Equations Educators