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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 259, Pages 106–133 (Mi tm572)  
This article is cited in 9 scientific papers (total in 10 papers)

New Methods for Proving the Existence and Stability of Periodic Solutions in Singularly Perturbed Delay Systems

A. Yu. Kolesova, E. F. Mishchenkob, N. Kh. Rozovc

a P. G. Demidov Yaroslavl State University
b Steklov Mathematical Institute, Russian Academy of Sciences
c M. V. Lomonosov Moscow State University
Full-text PDF (332 kB) Citations (10)
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Abstract: We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential–difference equation that is a mathematical model of a single-circuit $RCL$-oscillator with delay in a feedback loop.
Received in March 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 259, Pages 101–127
DOI: https://doi.org/10.1134/S0081543807040086
Bibliographic databases:
Document Type: Article
UDC: 517.926
Language: Russian
Citation: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “New Methods for Proving the Existence and Stability of Periodic Solutions in Singularly Perturbed Delay Systems”, Analysis and singularities. Part 2, Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 259, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 106–133; Proc. Steklov Inst. Math., 259 (2007), 101–127
Citation in format AMSBIB
\Bibitem{KolMisRoz07}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\paper New Methods for Proving the Existence and Stability of Periodic Solutions in Singularly Perturbed Delay Systems
\inbook Analysis and singularities. Part~2
\bookinfo Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2007
\vol 259
\pages 106--133
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm572}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2433680}
\zmath{https://zbmath.org/?q=an:05493532}
\elib{https://elibrary.ru/item.asp?id=9572731}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 259
\pages 101--127
\crossref{https://doi.org/10.1134/S0081543807040086}
\elib{https://elibrary.ru/item.asp?id=13538954}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38849092705}
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    • This publication is cited in the following 10 articles:
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