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Tr. Mat. Inst. 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

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 259, 101–127

Bibliographic databases:

UDC: 517.926
Received in March 2007

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, Tr. Mat. Inst. Steklova, 259, Nauka, MAIK Nauka/Inteperiodika, M., 2007, 106–133; Proc. Steklov Inst. Math., 259 (2007), 101–127

Citation in format AMSBIB
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\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 Tr. Mat. Inst. Steklova
\yr 2007
\vol 259
\pages 106--133
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm572}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 259
\pages 101--127
\crossref{https://doi.org/10.1134/S0081543807040086}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38849092705}


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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, “Extremal dynamics of the generalized Hutchinson equation”, Comput. Math. Math. Phys., 49:1 (2009), 71–83  mathnet  crossref  mathscinet  isi  elib  elib
    2. D. V. Glazkov, “Lokalnaya dinamika uravneniya s silno zapazdyvayuschei obratnoi svyazyu”, Model. i analiz inform. sistem, 18:1 (2011), 75–85  mathnet
    3. 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
    4. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Modeling the Bursting Effect in Neuron Systems”, Math. Notes, 93:5 (2013), 676–690  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. A. S. Bobok, S. D. Glyzin, A. Yu. Kolesov, “Ekstremalnaya dinamika sistemy trekh odnonapravlenno svyazannykh singulyarno vozmuschennykh uravnenii iz neirodinamiki”, Model. i analiz inform. sistem, 20:5 (2013), 158–167  mathnet
    6. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “The buffer phenomenon in ring-like chains of unidirectionally connected generators”, Izv. Math., 78:4 (2014), 708–743  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. M. M. Preobrazhenskaya, “Primenenie metoda kvazinormalnykh form k matematicheskoi modeli otdelnogo neirona”, Model. i analiz inform. sistem, 21:5 (2014), 38–48  mathnet
    8. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Self-excited relaxation oscillations in networks of impulse neurons”, Russian Math. Surveys, 70:3 (2015), 383–452  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Kornev S.V. Obukhovskii V.V. Zecca P., “Method of generalized integral guiding functions in the problem of the existence of periodic solutions for functional-differential inclusions”, Differ. Equ., 52:10 (2016), 1282–1292  crossref  mathscinet  zmath  isi  elib  scopus
    10. Glyzin S.D., Kolesov A.Yu., Preobrazhenskaia M.M., “Existence and Stability of Periodic Solutions of Quasi-Linear Korteweg - de Vries Equation”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012016  crossref  isi  scopus
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