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

## Description

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

# 3.9] 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.

Continue to: