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Nelin. Dinam., 2016, Volume 12, Number 1, Pages 121–143 (Mi nd516)  

This article is cited in 2 scientific papers (total in 2 papers)

Translated papers

Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

S. P. Kuznetsovab

a Kotelnikovs Institute of Radio Engineering and Electronics of RAS, Saratov Branch, 410019 Saratov, Zelenaya 38, Russian Federation
b Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: Dynamical equations are formulated and a numerical study is provided for selfoscillatory model systems based on the triple linkage hinge mechanism of ThurstonWeeksHuntMacKay. We consider systems with a holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.

Keywords: dynamical system, chaos, hyperbolic attractor, Anosov dynamics, rotator, Lyapunov exponent, self-oscillator

Funding Agency Grant Number
Russian Science Foundation 15-12-20035


Full text: PDF file (1998 kB)
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English version:
Regular and Chaotic Dynamics, 2015, 20:6, 649–666

UDC: 51-72, 514.85, 517.9, 534.1
MSC: 37D45, 37D20, 34D08, 32Q05, 70F20
Received: 28.09.2015
Revised: 30.10.2015

Citation: S. 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”, Nelin. Dinam., 12:1 (2016), 121–143; Regular and Chaotic Dynamics, 20:6 (2015), 649–666

Citation in format AMSBIB
\Bibitem{Kuz16}
\by S.~P.~Kuznetsov
\paper Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 1
\pages 121--143
\mathnet{http://mi.mathnet.ru/nd516}
\transl
\jour Regular and Chaotic Dynamics
\yr 2015
\vol 20
\issue 6
\pages 649--666
\crossref{https://doi.org/10.1134/S1560354715060027}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84948967074}


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    Translation

    This publication is cited in the following articles:
    1. 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
    2. S. P. Kuznetsov, “Khaos i giperkhaos geodezicheskikh potokov na mnogoobraziyakh s kriviznoi, otvechayuschikh mekhanicheski svyazannym rotatoram: primery i chislennoe issledovanie”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:4 (2018), 565–581  mathnet  crossref  elib
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