Geodesic
Hidden synchronization of phase-locked loops with nonlinear delay
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 88-96 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider a mathematical model of a phase locked loop system taking into account nonlinearity in the delay in the case of a fractional rational second-order integrating filter. We obtain conditions for the existence of several quasi-synchronous modes of the system, which determine the phase synchronization modes, and analyze the influence of the nonlinear delay on the phase multistability. We develop numerical and analytical conditions for the existence of hidden synchronization of phase systems and construct an algorithm for determining the influence of nonlinear delays on synchronization modes.
Keywords: phase system, phase locked loop, dynamic mode, self-modulation oscillations, synchronization. 
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     title = {Hidden synchronization of phase-locked loops with nonlinear delay},
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S. S. Mamonov; I. V. Ionova; A. O. Harlamova. Hidden synchronization of phase-locked loops with nonlinear delay. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 88-96. http://geodesic.mathdoc.fr/item/INTO_2022_216_a8/

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

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

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

[4] 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

[5] Mamonov S. S., Ionova I. V., Kharlamova A. O., “Matrichnye uravneniya sistem fazovoi sinkhronizatsii”, Chebyshevskii sb., 20:2 (2019), 244–258 | MR

[6] Mamonov S. S., Ionova I. V., Kharlamova A. O., “Prostranstvennye kharakteristiki tsiklov sistem differentsialnykh uravnenii”, Differentsialnye uravneniya i matematicheskoe modelirovanie. Vyp. 1, RGU im. S. A. Esenina, Ryazan, 2020, 39–45

[7] Mamonov S. S., Kharlamova A. O., “Vynuzhdennaya sinkhronizatsiya sistem fazovoi avtopodstroiki s zapazdyvaniem”, Vestn. Ryazan. gos. radiotekhn. un-ta., 2017, no. 62, 26–35

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

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

[10] Mamonov S. S., Kharlamova A. O., Ionova I. V., “Krivizna kolebatelnykh tsiklov fazovykh sistem”, Vestn. RAEN., 19:2 (2019), 105–110 | MR

[11] Kharlamova A. O., “Asinkhronnye rezhimy fazovykh sistem”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 148 (2018), 101–108

[12] Shakhgildyan V. V., Lyakhovkin A. A., Sistemy fazovoi avtopodstroiki chastoty, Svyaz, M., 1972