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Russian Journal of Nonlinear Dynamics, 2020, Volume 16, Number 1, Pages 51–58
DOI: https://doi.org/10.20537/nd200105 (Mi nd695) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Nonlinear physics and mechanics

Mechanical Systems with Hyperbolic Chaotic Attractors Based on Froude Pendulums

S. P. Kuznetsovab, V. P. Kruglovbc, Yu. V. Sedovab

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Saratov Branch of Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, ul. Zelenaya 38, Saratov, 410019 Russia
c Yuri Gagarin State Technical University, ul. Politechnicheskaya 77, Saratov, 410054 Russia
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DOI: https://doi.org/10.20537/nd200105
Abstract: We discuss two mechanical systems with hyperbolic chaotic attractors of Smale – Williams type. Both models are based on Froude pendulums. The first system is composed of two coupled Froude pendulums with alternating periodic braking. The second system is Froude pendulum with time-delayed feedback and periodic braking. We demonstrate by means of numerical simulations that the proposed models have chaotic attractors of Smale – Williams type. We specify regions of parameter values at which the dynamics corresponds to the Smale – Williams solenoid. We check numerically the hyperbolicity of the attractors.
Keywords: hyperbolic chaotic attractors, Smale – Williams solenoid, Bernoulli map.
Funding agency Grant number
Russian Science Foundation 15-12-20035
17-12-01008
S.P.Kuznetsov and V. P.Kruglov acknowledge support from the Russian Science Foundation, grant No. 15-12-20035 (Sections 1–3). Yu.V. Sedova acknowledges support from the Russian Science Foundation, grant No. 17-12-01008 (Section 4).
Received: 14.06.2019
Accepted: 09.09.2019
Bibliographic databases:
Document Type: Article
MSC: 37D05, 37D20, 37D45, 37M25, 34K23
Language: English
Citation: S. P. Kuznetsov, V. P. Kruglov, Yu. V. Sedova, “Mechanical Systems with Hyperbolic Chaotic Attractors Based on Froude Pendulums”, Rus. J. Nonlin. Dyn., 16:1 (2020), 51–58
Citation in format AMSBIB
\Bibitem{KuzKruSed20}
\by S. P. Kuznetsov, V. P. Kruglov, Yu. V. Sedova
\paper Mechanical Systems with Hyperbolic Chaotic Attractors Based on Froude Pendulums
\jour Rus. J. Nonlin. Dyn.
\yr 2020
\vol 16
\issue 1
\pages 51--58
\mathnet{http://mi.mathnet.ru/nd695}
\crossref{https://doi.org/10.20537/nd200105}
\elib{https://elibrary.ru/item.asp?id=43285483}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85084520841}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Russian Journal of Nonlinear Dynamics
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