Geodesic
Hidden synchronization in phase locked loop systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 168 (2019), pp. 71-79.

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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, beat mode, positively invariant set, rotation of a vector field.
Mots-clés : quasisynchronous mode 
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S. S. Mamonov; I. V. Ionova; A. O. Harlamova. Hidden synchronization in phase locked loop systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 168 (2019), pp. 71-79. http://geodesic.mathdoc.fr/item/INTO_2019_168_a8/

[1] Bakunov G. M., Matrosov V. V., Shalfeev V. D., “O kvazisinkhronnykh rezhimakh v sisteme fazovoi avtopodstroiki chastoty s filtrom vtorogo poryadka pri priblizhennom uchete zapazdyvaniya”, Izv. vuzov. Prikl. nelin. dinam., 19:3 (2011), 171–178 | Zbl

[2] Beskerskii V. A., Popov E. P., Teoriya sistem avtomaticheskogo regulirovaniya, Nauka, M., 1972

[3] Kapranov M. V., Kulishov V. N., Utkin G. M., Teoriya kolebanii v radiotekhnike, Nauka, M., 1984

[4] Krasnoselskii M. A., Operator sdviga po traektoriyam differentsialnykh uravnenii, Nauka, M., 1966 | MR

[5] Leonov G. A., Burkin I. M., Shepelyavyi A. I., Chastotnye metody v teorii kolebanii, Izd-vo SPbGU, SPb., 1992 | MR

[6] Mamonov S. S., “Dinamika sistemy chastotno-fazovoi avtopodstroiki chastoty s filtrami pervogo poryadka”, Vestn. Novosib. gos. un-ta. Ser. Mat. Mekh. Inform., 11:1 (2011), 70–81 | MR | Zbl

[7] Mamonov S. S., Ionova I. V., “Primenenie vrascheniya vektornogo polya dlya opredeleniya tsiklov vtorogo roda”, Vestn. RAEN. Differ. uravn., 14:5 (2014), 46–54

[8] Mamonov S. S., Kharlamova A. O., “Otdelenie tsiklov vtorogo roda sistemy chastotno-fazovoi avtopodstroiki chastoty”, Vestn. RAEN. Differ. uravn., 15:3 (2015), 97–102

[9] Mamonov S. S., Kharlamova A. O., “Kvazisinkhronnye rezhimy fazovoi sistemy”, Vestn. Ryazan. gos. radiotekhn. un-ta., 2016, no. 56, 45–51

[10] Mamonov S. S., Kharlamova A. O., “Opredelenie uslovii suschestvovaiya predelnykh tsiklov pervogo roda sistem s tsilindricheskim fazovym prostranstvom”, Zh. Srednevolzh. mat. o-va., 19:1 (2017), 67–76 | MR | Zbl

[11] Mamonov S. S., Kharlamova A. O., “Vynuzhdennaya sinkhronizatsiya sistem fazovoi avtopodstroiki s zapazdyvaniem”, Vestn. Ryazan. gos. radiotekhn. un-ta., 62 (2017), 26–35

[12] Mamonov S. S., Kharlamova A. O., “Chislenno-analiticheskoe opredelenie tsiklov pervogo roda fazovoi sistemy differentsialnykh uravnenii”, Vestn. RAEN. Differ. uravn., 17:4 (2017), 48–56 | MR

[13] Mamonov S. S., Kharlamova A. O., “Tsikly pervogo roda sistem s tsilindricheskim fazovym prostranstvom”, Itogi nauki i tekhn. Sovr. mat. prilozh. Temat. obzory., 148 (2018), 83–92 | MR

[14] Mamonov S. S., Kharlamova A. O., Ionova I. V., “Kolebatelno-vraschatelnye tsikly fazovoi sistemy differentsialnykh uravnenii”, Vestn. RAEN. Differ. uravn., 18:4 (2018), 51–57

[15] Matrosov V. V., Vynuzhdennaya sinkhronizatsiya, N. Novgorod, 2013

[16] Shalfeev V. D., Matrosov V. V., Nelineinaya dinamika v radiotekhnike, Izd-vo NNGU, N. Novgorod, 2013