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/