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# Hyperbolic chaos in systems with parametrically excited patterns of standing waves

2014, Vol. 10, No. 3, pp.  265-277

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

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