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Regul. Chaotic Dyn., 2016, Volume 21, Issue 2, Pages 160–174 (Mi rcd72)  

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

Funding Agency Grant Number
Russian Science Foundation 15-12-20035
This work was supported by RSF grant No 15-12-20035.


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}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84963761043}


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    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:
    1. P. V. Kuptsov, S. P. Kuznetsov, “Numerical test for hyperbolicity of chaotic dynamics in time-delay systems”, Phys. Rev. E, 94:1 (2016), 010201  crossref  isi  scopus
    2. 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  mathnet  crossref  elib
    3. 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  crossref  isi
    4. 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  crossref  mathscinet  isi  scopus
    5. 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  mathnet  crossref
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