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 m_{1}, m_{2}, α_{1}, and α_{2}. 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.

m_{1} =

m_{2} =

α_{1} =

α_{2} =

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

MathWorld's Phase Portrait

DFIELD & PPLANE -- web utilities

Community of Ordinary Differential Equations Educators