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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2019 Volume 168, Pages 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

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.

UDC: 517.925.51

MSC: 34K05, 34K13, 34K60

DOI: 10.36535/0233-6723-2019-168-71-79



© Steklov Math. Inst. of RAS, 2024