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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 168, Pages 71–79
DOI: https://doi.org/10.36535/0233-6723-2019-168-71-79 (Mi into502) 		 
Hidden synchronization in phase locked loop systems

S. S. Mamonov, I. V. Ionova, A. O. Harlamova

Ryazan State University S. A. Esenin
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DOI: https://doi.org/10.36535/0233-6723-2019-168-71-79
Abstract: This paper is devoted to the analysis of frequency-phase locked loop systems (FPLL). The mathematical model of this system is a system of differential equations with a cylindrical phase space. For the FPLL system, we obtain conditions of latent synchronization.
Keywords: hidden synchronization, frequency-phase locked loop, limit cycle of the first kind, quasisynchronous mode, beat mode, positively invariant set, rotation of a vector field.
Document Type: Article
UDC: 517.925.51
MSC: 34K05, 34K13, 34K60
Language: Russian
Citation: S. S. Mamonov, I. V. Ionova, A. O. Harlamova, “Hidden synchronization in phase locked loop systems”, Proceedings   of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 168, VINITI, Moscow, 2019, 71–79
Citation in format AMSBIB
\Bibitem{MamIonHar19}
\by S.~S.~Mamonov, I.~V.~Ionova, A.~O.~Harlamova
\paper Hidden synchronization in phase locked loop systems
\inbook Proceedings   of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25--28, 2018. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 168
\pages 71--79
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into502}
\crossref{https://doi.org/10.36535/0233-6723-2019-168-71-79}
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