Geodesic
Asynchronous Modes of Phase 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: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 101-108

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We consider a system of frequency-phase-locked loop whose mathematical model is described by a system of differential equations. In this paper, conditions of the existence of asynchronous modes of a phase system are obtained.
Keywords: system of differential equations, frequency ring, cycle of second kind, system of matrix equations, rotation of a vector field, trajectory shift operator, fixed point. 
@article{INTO_2018_148_a12,
     author = {A. O. Kharlamova},
     title = {Asynchronous {Modes} of {Phase} {Systems}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {101--108},
     publisher = {mathdoc},
     volume = {148},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_148_a12/}
}
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A. O. Kharlamova. Asynchronous Modes of Phase 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: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 101-108. http://geodesic.mathdoc.fr/item/INTO_2018_148_a12/