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




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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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