ul. Astrahanskaya 83, Saratov, 410012, Russia
Saratov State University
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
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.
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 $1:n$.