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2013
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    Alexey Kuznetsov

    Astrakhanskaya st. 83, Saratov, 410012, Russia
    Saratov State University

    Publications:

    Kuznetsov S. P., Kuznetsov A. S., Kruglov V. P.
    Abstract
    We outline a possibility of implementation of Smale–Williams type attractors with different stretching factors for the angular coordinate, namely, $n=3,\,5,\,7,\,9,\,11$, for the maps describing the evolution of parametrically excited standing wave patterns on a nonlinear string over a period of modulation of pump accompanying by alternate excitation of modes with the wavelength ratios of $1:n$.
    Keywords: parametric oscillations, string, attractor, chaos, Lyapunov exponent
    Citation: Kuznetsov S. P., Kuznetsov A. S., Kruglov V. P.,  Hyperbolic chaos in systems with parametrically excited patterns of standing waves, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 3, pp.  265-277
    DOI:10.20537/nd1403002
    Isaeva O. B., Kuznetsov A. S., Kuznetsov S. P.
    Abstract
    We outline a possibility of chaotic dynamics associated with a hyperbolic attractor of the Smale–Williams type in mechanical vibrations of a nonhomogeneous string with nonlinear dissipation arising due to parametric excitation of modes at the frequencies $\omega$ and $3\omega$, when the pump is supplied by means of the string tension variations alternately at frequencies of $2\omega$ and $6\omega$.
    Keywords: parametric oscillations, string, attractor, chaos, Lyapunov exponent
    Citation: Isaeva O. B., Kuznetsov A. S., Kuznetsov S. P.,  Hyperbolic chaos in parametric oscillations of a string, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 1, pp.  3-10
    DOI:10.20537/nd1301001

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