Alexey Kuznetsov
Publications:
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Kuznetsov S. P., Kuznetsov A. S., Kruglov V. P.
Hyperbolic chaos in systems with parametrically excited patterns of standing waves
2014, Vol. 10, No. 3, pp. 265-277
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 $1:n$.
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Isaeva O. B., Kuznetsov A. S., Kuznetsov S. P.
Hyperbolic chaos in parametric oscillations of a string
2013, Vol. 9, No. 1, pp. 3-10
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 $6\omega$.
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