Christophe LETELLIER
26/07/2020

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.**

[1] **A. S. Pikovsky & M. I. Rabinovich**, A simple autogenerator with stochastic behavior, *Dokladi Akademii Nauk SSSR*, **239**, 301-304, 1978.

[2] **J. Gao J., H. Lü, D. He, L. Stone & Z. Zheng**, Unexpected correspondence between noise-induced and master-slave complete synchronizations, *Physical Review E*, **68**, 037202, 2003.