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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 285, Pages 89–106
DOI: https://doi.org/10.1134/S0371968514020071 (Mi tm3538) 		 
This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (324 kB) Citations (5)
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DOI: https://doi.org/10.1134/S0371968514020071
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.
Received in February 2014
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 285, Pages 81–98
DOI: https://doi.org/10.1134/S0081543814040075
Bibliographic databases:
Document Type: Article
UDC: 517.926
Language: Russian
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, Trudy 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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\by S.~D.~Glyzin, A.~Yu.~Kolesov, N.~Kh.~Rozov
\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 Trudy 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
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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