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3.9] How can I build a chaotic circuit? (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.

3.9] How can I build a chaotic circuit? (nonlinear science)

(Thanks to Justin Lipton and Jose Korneluk for contributing to this answer)

There are many different physical systems which display chaos, dripping
faucets, water wheels, oscillating magnetic ribbons etc. but the most simple
systems which can be easily implemented are chaotic circuits. In fact an
electronic circuit was one of the first demonstrations of chaos which showed
that chaos is not just a mathematical abstraction. Leon Chua designed the
circuit 1983.

The circuit he designed, now known as Chua's circuit, consists of a piecewise
linear resistor as its nonlinearity (making analysis very easy) plus two
capacitors, one resistor and one inductor--the circuit is unforced
(autonomous). In fact the chaotic aspects (bifurcation values, Lyapunov
exponents, various dimensions etc.) of this circuit have been extensively
studied in the literature both experimentally and theoretically. It is
extremely easy to build and presents beautiful attractors (see [2.8]) (the
most famous known as the double scroll attractor) that can be displayed on a
CRO.

For more information on building such a circuit try: see

http://www.cmp.caltech.edu/~mcc/chaos_new/Chua.html Chua's Circuit Applet

References
Matsumoto T. and Chua L.O. and Komuro M. "Birth and Death of the Double
Scroll" Physica D24 97-124, 1987.
Kennedy M. P., "Robust OP Amp Realization of Chua's Circuit", Frequenz
46, no. 3-4, 1992
Madan, R. A., Chua's Circuit: A paradigm for chaos, ed. R. A. Madan,
Singapore: World Scientific, 1993.
Pecora, L. and Carroll, T. Nonlinear Dynamics in Circuits, Singapore:
World Scientific, 1995.
Nonlinear Dynamics of Electronic Systems, Proceedings of the Workshop
NDES 1993, A.C.Davies and W.Schwartz, eds., World Scientific, 1994,
ISBN 981-02-1769-2.
Parker, T.S., and L.O.Chua, Practical Numerical Algorithms for Chaotic
Systems, Springer-Verlag, 1989, ISBN's: 0-387-96689-7
and 3-540-96689-7.

 

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