Astrakhanskaya st. 83, Saratov, 410012, Russia
Saratov State University
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
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 $1:n$.
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
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 $6\omega$.