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A New Class of Chaotic Circuit

J. C. Sprott

*Department of Physics, University
of Wisconsin, Madison, Wisconsin 53706, USA*

(Received 30 November 1999; received in revised form 4 January 2000;
accepted 4 January 2000)
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ABSTRACT

A new class of chaotic electrical circuit using only resistors, capacitors,
diodes, and inverting operational amplifiers is described. This circuit
solves the equation *x*''' + *Ax*'' + *x*' = *G*(*x*),
where *G*(*x*) is one of a number of elementary piecewise linear
functions. These circuits are easy to construct and to scale over
a wide range of frequencies. They exhibit a variety of dynamical
behaviors and offer an excellent opportunity for detailed comparison with
theory.
Ref: J. C. Sprott, Phys. Lett. A **266**,
19-23 (2000)

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Fig. 1. A general circuit for solving Eq. (3) using one of the nonlinear
feedback elements in Fig. 2 for *G*(*x*).

Fig. 2. Some nonlinear forms for *G*(*x*) that produce chaos
and circuits to produce them.

Fig. 3. Chaotic attractors produced by each of the circuits in Fig.
2 in the *x*-*x*' plane. In the left-hand column are oscilloscope
traces, and in the right-hand column are the corresponding numerical solutions
on the same scale.