One-Dimensional Dynamical Systems
The study of one-dimensional discrete dynamical systems gives a
new interpretation to the investigation of functions defined on the
real line, namely the concept of iteration. Explorations are done
using the package Chaos.mpl in Maple. It is possible to use Java applets instead of Maple for
this course. These Java applets
are specified below.
John McDonald made the Java applet Iterates versus time for the Logistic map. You can set the number of iterates being shown and use sliders to vary the parameter .
There are other Java applets available on the web that let you explore the Logistic map. The applet Iteration of the Logistic Map of Andy Burbanks has sliders for changing the parameter and the starting point x0.
The second applet The Period Doubling Route to Chaos is written by Michael Cross. It accepts typed input, and it graphs the first, second and fourth iterates (and so on) of the logistic map. Complete instructions are given at the site, but you can also start with the abstracted instructions that show you how to do everything needed for this lab.
An almost complete set is provided at Boston University by Bob Devaney's group:
One-Dimensional Dynamical Systems was designed using