Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2017, Volume 13, Number 3, Pages 303–315
DOI: https://doi.org/10.20537/nd1703001 (Mi nd567) 		 
Original papers

Chaos generator with the Smale–Williams attractor based on oscillation death

V. M. Doroshenkoa, V. P. Kruglovb, S. P. Kuznetsovb

a Saratov State University, ul. Astrahanskaya 83, Saratov, 410012, Russia
b Saratov Branch of Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, ul. Zelenaya 38, Saratov, 410019, Russia
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DOI: https://doi.org/10.20537/nd1703001
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.
Funding agency Grant number
Russian Foundation for Basic Research 16-32-00449
Russian Science Foundation 17-12-01008
Received: 21.07.2017
Accepted: 31.08.2017
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 37D20, 37D45, 34C15, 34D08
Language: Russian
Citation: V. M. Doroshenko, V. P. Kruglov, S. P. Kuznetsov, “Chaos generator with the Smale–Williams attractor based on oscillation death”, Nelin. Dinam., 13:3 (2017), 303–315
Citation in format AMSBIB
\Bibitem{DorKruKuz17}
\by V.~M.~Doroshenko, V.~P.~Kruglov, S.~P.~Kuznetsov
\paper Chaos generator with the Smale–Williams attractor based on oscillation death
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 3
\pages 303--315
\mathnet{http://mi.mathnet.ru/nd567}
\crossref{https://doi.org/10.20537/nd1703001}
\elib{https://elibrary.ru/item.asp?id=29993262}
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