One-Dimensional Dynamical Systems
Part 2: Logistic Growth Model
Visualizing an orbit
Let us consider the evolution for p0 = 12, under
the assumption that the university campus provides essential needs for
maximally E = 200 squirrels. We set
= 2, which
corresponds to a growth rate of 1 baby per squirrel each year. What do
you expect to happen as the years go by? We can visualize the orbit of
p0 = 12 by plotting the iterates
pn against the years n. In the
following picture the evolution is shown over 100 years.
Logistic growth with growth factor = 2.
The picture shows a monotonic increase towards the saturation value E. It is suprising to see what happens if we vary , but still use E = 200 and p0 = 12. The following two pictures show the results over 100 years for = 3.1 and = 4. In the former case the population eventually oscillates between two different values. The latter case shows an unexpected, complicated behavior: chaos!
Logistic growth with growth factor = 3.1.
Logistic growth with growth factor = 4.
Written by Hinke Osinga
Comments to: email@example.com
Created: Apr 1 1998 --- Last modified: Wed Apr 8 18:10:03 1998