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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. O. Kharlamova
TI  - Asynchronous Modes of Phase Systems
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 101
EP  - 108
VL  - 148
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_148_a12/
LA  - ru
ID  - INTO_2018_148_a12
ER  - 
%0 Journal Article
%A A. O. Kharlamova
%T Asynchronous Modes of Phase Systems
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 101-108
%V 148
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_148_a12/
%G ru
%F INTO_2018_148_a12
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/

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

[2] Leonov G. A., Burkin I. M., Shepelyavyi A. I., Chastotnye metody v teorii kolebanii, Izd-vo SPbGU, SPb., 1992 | MR

[3] 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 | MR | Zbl

[4] Mamonov S. S., Ionova I. V., “Primenenie vrascheniya vektornogo polya dlya opredeleniya tsiklov vtorogo roda”, Vestn. RAEN. Differ. uravn., 14:5 (2014), 46–54

[5] Mamonov S. S., Kharlamova A. O., “Usloviya suschestvovaniya predelnykh tsiklov vtorogo roda dlya modeli sistemy chastotno-fazovoi avtopodstroiki chastoty”, Vestn. RAEN. Differ. uravn., 13:34 (2013), 51–57

[6] Mamonov S. S., Kharlamova A. O., “Vliyanie chastotnogo koltsa sistemy fazovoi avtopodstroiki na usloviya suschestvovaniya tsiklov vtorogo roda”, Vestn. RAEN. Differ. uravn., 14:5 (2014), 55–60

[7] Shalfeev V. D., Matrosov V. V., Nelineinaya dinamika sistem fazovoi sinkhronizatsii, Izd-vo NNGU, N. Novgorod., 2013