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Nelineinaya Dinamika
Article . 2019 . Peer-reviewed
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Nelineinaya Dinamika
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Article . 2019
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Generation of Robust Hyperbolic Chaos in CNN

Authors: Kuznetsov, Sergeĭ P.;

Generation of Robust Hyperbolic Chaos in CNN

Abstract

Summary: 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 \textsc{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.

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Keywords

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), attractor, chaos, cellular neural network, structural stability, Generic properties, structural stability of dynamical systems, Stability theory for smooth dynamical systems, pattern, Strange attractors, chaotic dynamics of systems with hyperbolic behavior

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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