Chaos generator with the Smale–Williams attractor based on oscillation death

    Received 21 July 2017; accepted 30 August 2017

    2017, Vol. 13, No. 3, pp.  303-315

    Author(s): Doroshenko V. M., Kruglov V. P., Kuznetsov S. P.

    A nonautonomous system with a uniformly hyperbolic attractor of Smale – Williams type in a Poincaré cross-section is proposed with generation implemented on the basis of the effect of oscillation death. The results of a numerical study of the system are presented: iteration diagrams for phases and portraits of the attractor in the stroboscopic Poincaré cross-section, power density spectra, Lyapunov exponents and their dependence on parameters, and the atlas of regimes. The hyperbolicity of the attractor is verified using the criterion of angles.
    Keywords: uniformly hyperbolic attractor, Smale–Williams solenoid, Bernoulli map, oscillation death, Lyapunov exponents
    Citation: Doroshenko V. M., Kruglov V. P., Kuznetsov S. P., Chaos generator with the Smale–Williams attractor based on oscillation death, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 3, pp.  303-315
    DOI:10.20537/nd1703001


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