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)
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
Ref: J. C. Sprott, Phys. Lett. A 266,
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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.