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Tr. Mat. Inst. Steklova, 2014, Volume 285, Pages 89–106 (Mi tm3538)  

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

Autowave processes in continual chains of unidirectionally coupled oscillators

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University, Yaroslavl, Russia
b M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: We introduce a mathematical model of a continual circular chain of unidirectionally coupled oscillators. It is a nonlinear hyperbolic boundary value problem obtained from a circular chain of unidirectionally coupled ordinary differential equations in the limit as the number of equations indefinitely increases. We study the attractors of this boundary value problem. Combining analytic and numerical methods, we establish that one of the following two alternatives takes place in this problem: either the buffer phenomenon (unbounded accumulation of stable periodic motions) or chaotic attractors of arbitrarily high Lyapunov dimensions.

DOI: https://doi.org/10.1134/S0371968514020071

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 285, 81–98

Bibliographic databases:

Document Type: Article
UDC: 517.926
Received in February 2014

Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Autowave processes in continual chains of unidirectionally coupled oscillators”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Tr. Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 89–106; Proc. Steklov Inst. Math., 285 (2014), 81–98

Citation in format AMSBIB
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\paper Autowave processes in continual chains of unidirectionally coupled oscillators
\inbook Selected topics of mathematical physics and analysis
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 285
\pages 89--106
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3538}
\crossref{https://doi.org/10.1134/S0371968514020071}
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\jour Proc. Steklov Inst. Math.
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\pages 81--98
\crossref{https://doi.org/10.1134/S0081543814040075}
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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. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Avtovolnovye protsessy v koltsevoi neironnoi tsepi s odnonapravlennoi svyazyu”, Model. i analiz inform. sistem, 22:3 (2015), 404–419  mathnet  crossref  mathscinet  elib
    2. S. D. Glyzin, S. A. Kaschenko, A. O. Tolbei, “Vzaimodeistvie dvukh voln v modeli Fermi–Pasta–Ulama”, Model. i analiz inform. sistem, 23:5 (2016), 548–558  mathnet  crossref  mathscinet  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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