**Up:** *Logistic Growth Model*

# One-Dimensional Dynamical Systems

## Part 2: Logistic Growth Model

#### Visualizing an orbit

Let us consider the evolution for *p*_{0} = 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
*p*_{0} = 12 by plotting the iterates
*p*_{n} 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 *p*_{0} = 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.*

**Up:** *Logistic Growth Model*

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Created: Apr 1 1998 ---
Last modified: Wed Apr 8 18:10:03 1998