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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 5, Pages 82–94 (Mi timm611)  

This article is cited in 1 scientific paper (total in 2 paper)

Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators

A. Yu. Kolesova, E. F. Mishchenko, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University, Faculty of Pedagogical Education

Abstract: We consider a two-dimensional lattice of the coupled van der Pol oscillators obtained by the standard space discretization of a nonlinear wave equation
$$ u_{tt}+\varepsilon(u^2-1)u_t+u=a_1^2u_{xx}+a_2^2u_{yy},\qquad a_1,a_2=const>0,\quad0<\varepsilon\ll1, $$
in the unit square subject to the zero Neumann boundary conditions. We prove that the related system of ordinary differential equations owns attractors which have not analogues in the original boundary problem. They are stable invariant tori of different dimensions. It is shown that the number of this tori grows without limit as the number of equations in the lattice increases.

Keywords: lattice of connected oscillators, invariant torus, attractor, bufferness.

Full text: PDF file (213 kB)
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UDC: 517.926
Received: 10.12.2009

Citation: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 5, 2010, 82–94

Citation in format AMSBIB
\Bibitem{KolMisRoz10}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\paper Multifrequency self-oscillations in two-dimensional lattices of coupled oscillators
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 5
\pages 82--94
\mathnet{http://mi.mathnet.ru/timm611}
\elib{http://elibrary.ru/item.asp?id=15265835}


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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. D. V. Anosov, S. M. Aseev, R. V. Gamkrelidze, S. P. Konovalov, M. S. Nikol'skii, N. Kh. Rozov, “Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)”, Russian Math. Surveys, 67:2 (2012), 385–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. S. Bobok, S. D. Glyzin, “Avtokolebaniya reshetok nelineinykh elementov v opyte Skotta”, Model. i analiz inform. sistem, 19:5 (2012), 56–68  mathnet
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