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).   no is the input nutrient concentration.   D is the dilution rate.  : The bacterial population grows at a rate modeled by Michaelis-Menten dynamics -- kmax is the maximum growth rate, kn 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:

The user inputs values of the parameters kmax, kn, D, no, and β. 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.

kmax =  

kn =  

D =  

no =  

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