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Nelin. Dinam., 2013, Volume 9, Number 1, Pages 3–10 (Mi nd365)  

This article is cited in 6 scientific papers (total in 6 papers)

Hyperbolic chaos in parametric oscillations of a string

Olga B. Isaevaab, Alexey S. Kuznetsovb, Sergey P. Kuznetsovab

a Saratov Branch of Kotelnikovs Institute of Radio-Engineering and Electronics of RAS, Saratov,  Russia
b Saratov State University, Saratov,  Russia

Abstract: We outline a possibility of chaotic dynamics associated with a hyperbolic attractor of the Smale–Williams type in mechanical vibrations of a nonhomogeneous string with nonlinear dissipation arising due to parametric excitation of modes at the frequencies $\omega$ and $3\omega$, when the pump is supplied by means of the string tension variations alternately at frequencies of $2\omega$ and $6\omega$.

Keywords: parametric oscillations, string, attractor, chaos, Lyapunov exponent.

Full text: PDF file (529 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.9+534
MSC: 37D20, 37D45, 37L30, 37L45
Received: 10.01.2013
Revised: 27.02.2013

Citation: Olga B. Isaeva, Alexey S. Kuznetsov, Sergey P. Kuznetsov, “Hyperbolic chaos in parametric oscillations of a string”, Nelin. Dinam., 9:1 (2013), 3–10

Citation in format AMSBIB
\Bibitem{IsaKuzKuz13}
\by Olga~B.~Isaeva, Alexey~S.~Kuznetsov, Sergey~P.~Kuznetsov
\paper Hyperbolic chaos in parametric oscillations of a string
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 1
\pages 3--10
\mathnet{http://mi.mathnet.ru/nd365}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Kruglov, A. S. Kuznetsov, S. P. Kuznetsov, “Giperbolicheskii khaos v sistemakh s parametricheskim vozbuzhdeniem patternov stoyachikh voln”, Nelineinaya dinam., 10:3 (2014), 265–277  mathnet
    2. Vyacheslav P. Kruglov, Sergey P. Kuznetsov, Arkady Pikovsky, “Attractor of SmaleWilliams Type in an Autonomous Distributed System”, Regul. Chaotic Dyn., 19:4 (2014), 483–494  mathnet  crossref  mathscinet  zmath
    3. Sergey P. Kuznetsov, “Hyperbolic Chaos in Self-oscillating Systems Based on Mechanical Triple Linkage: Testing Absence of Tangencies of Stable and Unstable Manifolds for Phase Trajectories”, Regul. Chaotic Dyn., 20:6 (2015), 649–666  mathnet  crossref  mathscinet  adsnasa
    4. 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  mathnet  crossref  mathscinet
    5. S. P. Kuznetsov, V. P. Kruglov, “On some simple examples of mechanical systems with hyperbolic chaos”, Proc. Steklov Inst. Math., 297 (2017), 208–234  mathnet  crossref  crossref  mathscinet  isi  elib
    6. R. M. Rozental, O. B. Isaeva, N. S. Ginzburg, I. V. Zotova, A. S. Sergeev, A. G. Rozhnev, “Characteristics of Chaotic Regimes in a Space-distributed Gyroklystron Model with Delayed Feedback”, Nelineinaya dinam., 14:2 (2018), 155–168  mathnet  crossref
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