RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Nelin. Dinam., 2014, Volume 10, Number 3, Pages 265–277 (Mi nd442)  

This article is cited in 3 scientific papers (total in 3 papers)

Hyperbolic chaos in systems with parametrically excited patterns of standing waves

Vyacheslav P. Kruglovab, Alexey S. Kuznetsova, Sergey P. Kuznetsovab

a Kotelnikovs Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019 Russia
b Saratov State University, Astrahanskaya 83, Saratov, 410012, Russia

Abstract: We outline a possibility of implementation of Smale–Williams type attractors with different stretching factors for the angular coordinate, namely, $n = 3,5,7,9,11$, for the maps describing the evolution of parametrically excited standing wave patterns on a nonlinear string over a period of modulation of pump accompanying by alternate excitation of modes with the wavelength ratios of $1:n$.

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

Full text: PDF file (998 kB)
References: PDF file   HTML file
UDC: 517.9+534
MSC: 37D20, 37D45, 37L30, 37L45
Received: 05.09.2014
Revised: 18.09.2014

Citation: Vyacheslav P. Kruglov, Alexey S. Kuznetsov, Sergey P. Kuznetsov, “Hyperbolic chaos in systems with parametrically excited patterns of standing waves”, Nelin. Dinam., 10:3 (2014), 265–277

Citation in format AMSBIB
\Bibitem{KruKuzKuz14}
\by Vyacheslav~P.~Kruglov, Alexey~S.~Kuznetsov, Sergey~P.~Kuznetsov
\paper Hyperbolic chaos in systems with parametrically excited patterns of~standing waves
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 3
\pages 265--277
\mathnet{http://mi.mathnet.ru/nd442}


Linking options:
  • http://mi.mathnet.ru/eng/nd442
  • http://mi.mathnet.ru/eng/nd/v10/i3/p265

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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
    2. 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
    3. 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
  • Number of views:
    This page:196
    Full text:49
    References:39

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020