A Basic Chemostat with Predator-Prey Bacteria Populations -- Non-Dimensional Form
by Mike Martin

On this page, plots of solutions for a simple chemostat model for predator-prey bacteria populations that has been non-dimensionalized (variable transformations are utilized so that the number of parameters can be minimized).   The equations for this chemostat model are:

Plots of the non-dimensionalized bacteria and nutrient concentrations are given below and the phase portrait (for the x and y variables, the bacteria population measures) with stream lines is below the concentration plots.   The species with population measure y is a predator on the species with population measure x.   The user inputs values of the parameters m1, m2, α1, and α2. Also, gird bounds, time bounds, and the initial conditions must be specified. S represents a measure of the nutrient concentration.



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

m1 =  

m2 =  

α1 =  

α2 =  


S (0) = 1 - x (0) - y (0)

x (0) =  

y (0) =  


0   ≤   t   ≤  


  ≤   x   ≤  

  ≤   y   ≤  


References:

Wikipedia's Phase Portrait

MathWorld's Phase Portrait

DFIELD & PPLANE -- web utilities

Community of Ordinary Differential Equations Educators