A Basic Chemostat by Mike Martin

On this page, plots of solutions for a simple chemostat model. The nutrient concentration is represented by n (t) and the concentration of the bacteria is represented by b (t). n_{o} is the input nutrient concentration. D is the dilution rate. : The bacterial population grows at a rate modeled by Michaelis-Menten dynamics -- k_{max} is the maximum growth rate, k_{n} is the half-saturation constant, and 1 / β is the yield. Plots of the bacterial and nutrient concentrations are given below and the phase portrait with stream lines is below the concentration plots. The equations are of the form:

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

k_{max} =

k_{n} =

D =

n_{o} =

β =

b (0) =

n (0) =

0 ≤ t ≤

≤ b ≤

≤ n ≤

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