Consider the continuous anolog of the logistic model using the
ODE:
x' = r x (1 - x/k)
where x(t) is the population size
at time t, r (growth rate) and k (carrying capacity) are parameters.
For r = 1 and k = 1.5, several solutions of this equation with various initial conditions
are displayed in the picture below. Describe what happens to the population
as the initial population size varies.
Download the following phaser Project file
logisticODE.ppf
by just clicking on it
( or by right-click and save it to our computer. Now load this file into Phaser).
You should see the following XivsTime view:
Fix the parameter r = 1 and vary the parameter k from 0.5 to 3.0.
Next fix k = 1.5 and vary r from 0.5 to 4.0. Describe the results of your experiments
from the biological viewpoint.