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.
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).
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
\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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https://www.mathnet.ru/eng/nd695
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This publication is cited in the following 3 articles:
Vyacheslav Kruglov, Igor Sataev, “On hyperbolic attractors in a modified complex Shimizu–Morioka system”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 33:6 (2023)
Grzegorz Litak, Marek Borowiec, Krzysztof Da̧bek, “Dynamics and Entropy Analysis of a Frictionally Loaded Pendulum”, Entropy, 24:9 (2022), 1269
S. P. Kuznetsov, V. P. Kruglov, I. R. Sataev, “Smale-Williams solenoids in autonomous system with saddle equilibrium”, Chaos, 31:1 (2021), 013140
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