Up: Logistic Growth Model

# 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.

Up: Logistic Growth Model The Geometry Center Home Page

Written by Hinke Osinga