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In this paper, we consider a system of differential equations describing a mathematical model of a phase-locked loop with a delay. We introduce the concept of the curvature of a cycle, which is applied to analyzing the proximity of cycles of nonphase and phase systems. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of frequency-phase locked loop systems (FPLL). The mathematical model of such systems is a system of differential equations with a cylindrical phase space. For FPLL systems, we obtain conditions of latent synchronization. [ABSTRACT FROM AUTHOR]

We consider a system of frequency-phase self-tuning whose mathematical model is a system of differential equations. In this paper, existence conditions for asynchronous modes of a phase system are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of differential equations with a cylindrical phase space, which is a mathematical model of a phase-locked loop system. Conditions of the existence of limit cycle of the first kind are obtained. [ABSTRACT FROM AUTHOR]