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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, and elaborate on the concept of iteration of functions. Explorations are done using the package Chaos.m in Mathematica, or Chaos and Dynamics (for Macintosh computers), and three Java applets.


Table of Contents:


Java Applets

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 lambda.

There are two 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 lambda and the starting point x0. See also the local copy.

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.


References

One-Dimensional Dynamical Systems was designed using

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Written by Hinke Osinga
Comments to: webmaster@geom.umn.edu
Created: Mar 31 1998 --- Last modified: Mon May 18 16:24:26 1998