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 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).
[Figure 1]

Fig. 2. Some nonlinear forms for G(x) that produce chaos and circuits to produce them.
[Figure 2]
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.
[Figure 3]