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2013
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# Vyacheslav Kruglov

Zelenaya 38, Saratov, 410019, Russia
IRE RAS Saratov branch

## Publications:

 Doroshenko V. M., Kruglov V. P., Kuznetsov S. P. Chaos generator with the Smale–Williams attractor based on oscillation death 2017, Vol. 13, No. 3, pp.  303-315 Abstract A nonautonomous system with a uniformly hyperbolic attractor of Smale – Williams type in a Poincaré cross-section is proposed with generation implemented on the basis of the effect of oscillation death. The results of a numerical study of the system are presented: iteration diagrams for phases and portraits of the attractor in the stroboscopic Poincaré cross-section, power density spectra, Lyapunov exponents and their dependence on parameters, and the atlas of regimes. The hyperbolicity of the attractor is verified using the criterion of angles. Keywords: uniformly hyperbolic attractor, Smale–Williams solenoid, Bernoulli map, oscillation death, Lyapunov exponents Citation: Doroshenko V. M., Kruglov V. P., Kuznetsov S. P.,  Chaos generator with the Smale–Williams attractor based on oscillation death, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 3, pp.  303-315 DOI:10.20537/nd1703001
 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 $1:n$. 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