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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 3, Pages 123–138
DOI: https://doi.org/10.33048/SIBJIM.2020.23.310 (Mi sjim1103) 		 
Nonlinear oscillations in the clock frequency generator excited by a sequence of concentrated electrostatic pulses coordinated with the oscillations

S. I. Fadeevab

a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.310
Abstract: Under consideration is the mathematical model of a clock frequency generator in which some high-frequency oscillations of a movable electrode are excited by a sequence of concentrated electrostatic pulses; wherein the times of pulse action are coordinated with the oscillations of the movable electrode by analogy with the well-known theory of a trigger clock. The results of studying the mathematical model provide a fairly complete understanding of the properties of the oscillations that are excited in the generator.
Keywords: mathematical model, frequency generator, periodic oscillations, limit cycle, stability, phase plane, boundary value problem, continuation of a solution with respect to a parameter. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0013
The author is grateful to E. G. Kostsov and A. A. Sokolov for effective discussions of the mathematical model of a generator.
Received: 26.12.2019
Revised: 26.12.2019
Accepted: 09.04.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 3, Pages 443–455
DOI: https://doi.org/10.1134/S1990478920030047
Bibliographic databases:
Document Type: Article
UDC: 519.62:621.38
Language: Russian
Citation: S. I. Fadeev, “Nonlinear oscillations in the clock frequency generator excited by a sequence of concentrated electrostatic pulses coordinated with the oscillations”, Sib. Zh. Ind. Mat., 23:3 (2020), 123–138; J. Appl. Industr. Math., 14:3 (2020), 443–455
Citation in format AMSBIB
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\by S.~I.~Fadeev
\paper Nonlinear oscillations in the clock frequency generator
excited by a sequence of concentrated electrostatic pulses
coordinated with the oscillations
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 3
\pages 123--138
\mathnet{http://mi.mathnet.ru/sjim1103}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.310}
\elib{https://elibrary.ru/item.asp?id=45220808}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 3
\pages 443--455
\crossref{https://doi.org/10.1134/S1990478920030047}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85094653437}
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