# 3.10] What are simple experiments to demonstrate chaos? (nonlinear science)

## Description

This article is from the Nonlinear Science FAQ, by James D. Meiss jdm@boulder.colorado.edu with numerous contributions by
others.

# 3.10] What are simple experiments to demonstrate chaos? (nonlinear science)

There are many "chaos toys" on the market. Most consist of some sort of

pendulum that is forced by an electromagnet. One can of course build a simple

double pendulum to observe beautiful chaotic behavior see

http://quasar.mathstat.uottawa.ca/~selinger/lagrange/doublependulum.html

Experimental Pendulum Designs

http://www.maths.tcd.ie/~plynch/SwingingSpring/doublependulum.html Java

Applet

http://monet.physik.unibas.ch/~elmer/pendulum/ Java Applets Pendulum Lab

My favorite double pendulum consists of two identical planar pendula, so that

you can demonstrate sensitive dependence [2.10], for a Java applet simulation

see http://www.cs.mu.oz.au/~mkwan/pendulum/pendulum.html. Another cute toy is

the "Space Circle" that you can find in many airport gift shops. This is

discussed in the article:

A. Wolf & T. Bessoir, Diagnosing Chaos in the Space Circle, Physica 50D,

1991.

One of the simplest chemical systems that shows chaos is the Belousov-

Zhabotinsky reaction. The book by Strogatz [4.1] has a good introduction to

this subject,. For the recipe see

http://www.ux.his.no/~ruoff/BZ_Phenomenology.html. Chemical chaos is modeled

(in a generic sense) by the "Brusselator" system of differential equations.

See

Nicolis, Gregoire & Prigogine, (1989) Exploring Complexity: An

Introduction W. H. Freeman

The Chaotic waterwheel, while not so simple to build, is an exact realization

of Lorenz famous equations. This is nicely discussed in Strogatz book [4.1] as

well.

Billiard tables can exhibit chaotic motion, see

http://www.maa.org/mathland/mathland_3_3.html, though it might be hard to see

this next time you are in a bar, since a rectangular table is not chaotic!

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