|
This article is cited in 5 scientific papers (total in 5 papers)
Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics
Sergey P. Kuznetsovabc, Vyacheslav P. Kruglovcb a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
b Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019, Russia
c Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia
Abstract:
Computer verification of hyperbolicity is provided based on statistical analysis of the angles of intersection of stable and unstable manifolds for mechanical systems with hyperbolic attractors of Smale – Williams type: (i) a particle sliding on a plane under periodic kicks, (ii) interacting particles moving on two alternately rotating disks, and (iii) a string with parametric excitation of standing-wave patterns by a modulated pump. The examples are of interest as contributing to filling the hyperbolic theory of dynamical systems with physical content.
Keywords:
dynamical system, chaos, attractor, hyperbolic dynamics, Lyapunov exponent, Smale – Williams solenoid, parametric oscillations
DOI:
https://doi.org/10.1134/S1560354716020027
References:
PDF file
HTML file
Bibliographic databases:
MSC: 37D20, 37D45, 70G60, 70Q05 Received: 06.12.2015 Accepted:15.02.2016
Language:
Citation:
Sergey P. Kuznetsov, Vyacheslav P. Kruglov, “Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 160–174
Citation in format AMSBIB
\Bibitem{KuzKru16}
\by Sergey P. Kuznetsov, Vyacheslav P. Kruglov
\paper Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 2
\pages 160--174
\mathnet{http://mi.mathnet.ru/rcd72}
\crossref{https://doi.org/10.1134/S1560354716020027}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3486003}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000374286800002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84963761043}
Linking options:
http://mi.mathnet.ru/eng/rcd72 http://mi.mathnet.ru/eng/rcd/v21/i2/p160
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
P. V. Kuptsov, S. P. Kuznetsov, “Numerical test for hyperbolicity of chaotic dynamics in time-delay systems”, Phys. Rev. E, 94:1 (2016), 010201
-
V. M. Doroshenko, V. P. Kruglov, S. P. Kuznetsov, “Generator khaosa s attraktorom Smeila–Vilyamsa na osnove effekta gibeli kolebanii”, Nelineinaya dinam., 13:3 (2017), 303–315
-
V. M. Doroshenko, V. P. Kruglov, M. V. Pozdnyakov, “Robust chaos in systems of circular geometry”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 3122–3128
-
P. V. Kuptsov, S. P. Kuznetsov, “Numerical test for hyperbolicity in chaotic systems with multiple time delays”, Commun. Nonlinear Sci. Numer. Simul., 56 (2018), 227–239
-
S. P. Kuznetsov, V. P. Kruglov, V. M. Doroshenko, “Smale–Williams Solenoids in a System of Coupled Bonhoeffer–van der Pol Oscillators”, Nelineinaya dinam., 14:4 (2018), 435–451
|
Number of views: |
This page: | 105 | References: | 24 |
|