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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 512, Pages 69–77
DOI: https://doi.org/10.31857/S2686954323600106 (Mi danma401) 		 
This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

Hidden boundary of global stability in the Kapranov conjecture on the pull-in range

N. Kuznetsovab, M. Yu. Lobacheva, T. N. Mokaeva

a Saint Petersburg State University
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
Citations (5)
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DOI: https://doi.org/10.31857/S2686954323600106
Abstract: Within the framework of the development of the theory of hidden oscillations, the problem of determining the boundary of global stability and revealing its hidden parts corresponding to the non-local birth of hidden oscillations is considered. For a phase-locked loop with a proportional-integrating filter and a piecewise-linear phase detector characteristic, effective methods for determination of bifurcations of the global stability loss, for obtaining analytical formulas of the bifurcation values, and for constructing trivial and hidden parts of the global stability boundary are suggested.
Keywords: hidden boundary of global stability, self-excited and hidden oscillations, local and global bifurcations, phase-locked loop, Kapranov conjecture, pull-in range.
Funding agency Grant number
Russian Science Foundation 22-11-00172
This work was supported by the Russian Science Foundation, project no. 22-11-00172.
Received: 25.02.2023
Revised: 12.05.2023
Accepted: 22.05.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 1, Pages 300–308
DOI: https://doi.org/10.1134/S1064562423700898
Bibliographic databases:
Document Type: Article
UDC: 531.36:534.1
Language: Russian
Citation: N. Kuznetsov, M. Yu. Lobachev, T. N. Mokaev, “Hidden boundary of global stability in the Kapranov conjecture on the pull-in range”, Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023), 69–77; Dokl. Math., 108:1 (2023), 300–308
Citation in format AMSBIB
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\by N.~Kuznetsov, M.~Yu.~Lobachev, T.~N.~Mokaev
\paper Hidden boundary of global stability in the Kapranov conjecture on the pull-in range
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 512
\pages 69--77
\mathnet{http://mi.mathnet.ru/danma401}
\crossref{https://doi.org/10.31857/S2686954323600106}
\elib{https://elibrary.ru/item.asp?id=54538898}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 1
\pages 300--308
\crossref{https://doi.org/10.1134/S1064562423700898}
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    • This publication is cited in the following 5 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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