1978 A simple autogenerator of chaotic behaviors

In the 1970s, new ideas about the transition to turbulence emerged. In particular, it seemed possible to produce chaotic oscillations with three-dimensional dynamical systems. These ideas triggered the search for an electronic circuit producing these chaotic oscillations. Arkady S. Pikovsky and Mikhail Rabinovich designed one which resembles to a van der Pol generator with an additional active element. [1] It includes a negative conductance -g and a tunnler diode whose characteristic is the cubic function

A sketch of the electronic circuit is shown in Fig. 1.

Fig. 1. Electronic circuit of the simple autogenerator.

The governing equations are

With the parameter values [2]

the autogenerators produces a two-scroll attractor (Fig. 2).

Fig. 2. Double-scroll attractor produced by the Pikovsky-Rabinovich autogenerator.