Much recent interest has been given to simple chaotic
oscillators based on jerk equations that involve a third-time
derivative of a single scalar variable. The simplest such
equation has yet to be electronically implemented. This paper
describes a particularly elegant circuit whose operation is
accurately described by a simple variant of that equation in
which the requisite nonlinearity is provided by a single diode
and for which the analysis is particularly straightforward.

(Manuscript received September 20, 2010; revised December 1, 2010;
accepted January 26, 2011. Date of current version April 20,
2011.)Ref: J.
C. Sprott, IEEE Transactions on Circuits and Systems--II:
Express Briefs 58,
240-243 (2011)

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Fig. 1. Chaotic
circuit schematic.

Fig. 2. Actual circuit in operation.

Fig. 3. Frequency spectrum of the*x* output of the chaotic
circuit.

Fig. 4. Numerically calculated phase space plot on the same scale as Fig. 2.

Fig. 5. Numerically calculated waveforms of*x* and its
successive derivatives.

Fig. 6. Poincaré section in the x-y plane at the instant of maximum diode conduction.

Fig. 7. Largest Lyapunov exponent and the value of*x* when
*dx/dt* is a local maximum versus the bifurcation parameter *A*
in (6).

Fig. 8. Homoclinic orbits, with the upper for*A* = 0.7043
and the lower for *A* = 0.3890 in (6).

Fig. 2. Actual circuit in operation.

Fig. 3. Frequency spectrum of the

Fig. 4. Numerically calculated phase space plot on the same scale as Fig. 2.

Fig. 5. Numerically calculated waveforms of

Fig. 6. Poincaré section in the x-y plane at the instant of maximum diode conduction.

Fig. 7. Largest Lyapunov exponent and the value of

Fig. 8. Homoclinic orbits, with the upper for