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1978 A simple autogenerator of chaotic behaviors

Christophe LETELLIER
26/07/2020
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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.

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Fig. 1. Electronic circuit of the simple autogenerator.

The governing equations are

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With the parameter values [2]

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

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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.

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