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 Nelin. Dinam., 2019, Volume 15, Number 2, Pages 109–124 (Mi nd645)

Nonlinear physics and mechanics

Generation of Robust Hyperbolic Chaos in CNN

S. P. Kuznetsov

Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov Branch, ul. Zelenaya 38, Saratov, 410019 Russia

Abstract: It is shown that on the basis of a cellular neural network (CNN) composed, e.g., of six cells, it is possible to design a chaos generator with an attractor being a kind of Smale – Williams solenoid, which provides chaotic dynamics that is rough (structurally stable), as follows from respective fundamental mathematical theory. In the context of the technical device, it implies insensitivity to small variations of parameters, manufacturing imperfections, interferences, etc. Results of numerical simulations and circuit simulation in the Multisim environment are presented. The proposed circuit is the first example of an electronic system where the role of the angular coordinate for the Smale – Williams attractor is played by the spatial phase of the sequence of patterns. It contributes to the collection of feasible systems with hyperbolic attractors and thus promotes filling with real content and promises practical application for the hyperbolic theory, which is an important and deep sector of the modern mathematical theory of dynamical systems.

Keywords: cellular neural network, chaos, attractor, pattern, dynamics, structural stability

 Funding Agency Grant Number Russian Academy of Sciences - Federal Agency for Scientific Organizations The work was carried out within the framework of the state task of Kotel’nikov’s IRE RAS.

DOI: https://doi.org/10.20537/nd190201

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MSC: 37D20, 37D45, 70K75, 94C99
Accepted:02.05.2019

Citation: S. P. Kuznetsov, “Generation of Robust Hyperbolic Chaos in CNN”, Nelin. Dinam., 15:2 (2019), 109–124

Citation in format AMSBIB
\Bibitem{Kuz19} \by S. P. Kuznetsov \paper Generation of Robust Hyperbolic Chaos in CNN \jour Nelin. Dinam. \yr 2019 \vol 15 \issue 2 \pages 109--124 \mathnet{http://mi.mathnet.ru/nd645} \crossref{https://doi.org/10.20537/nd190201}