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JOURNALS // Russian Journal of Nonlinear Dynamics // Archive

Nelin. Dinam., 2014 Volume 10, Number 3, Pages 265–277 (Mi nd442)

This article is cited in 6 papers

Hyperbolic chaos in systems with parametrically excited patterns of standing waves

Vyacheslav P. Kruglovab, Alexey S. Kuznetsova, Sergey P. Kuznetsovab

a Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019 Russia
b Saratov State University, Astrahanskaya 83, Saratov, 410012, Russia

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.

UDC: 517.9+534

MSC: 37D20, 37D45, 37L30, 37L45

Received: 05.09.2014
Revised: 18.09.2014



© Steklov Math. Inst. of RAS, 2025