Generation of Robust Hyperbolic Chaos in CNN

    Received 15 April 2019

    2019, Vol. 15, no. 2, pp.  109-124

    Author(s): Kuznetsov S. P.

    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
    Citation: Kuznetsov S. P., Generation of Robust Hyperbolic Chaos in CNN, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 2, pp.  109-124

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