Geodesic
Cycles of the First Kind of Systems with Cylindrical Phase Space
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. 83-92.

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

In this paper, we consider a system of differential equations with a cylindrical phase space, which is a mathematical model of a frequency-phase self-tuning system. Conditions for the existence of a limit cycle of the first kind are obtained.
Keywords: limit cycle of the first kind, cylindrical phase space, positively invariant set, toroidal set. 
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S. S. Mamonov; A. O. Kharlamova. Cycles of the First Kind of Systems with Cylindrical Phase Space. 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. 83-92. http://geodesic.mathdoc.fr/item/INTO_2018_148_a10/

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

[2] 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

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

[4] 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

[5] Mamonov S. S., Kharlamova A. O., “Otdelenie tsiklov vtorogo roda sistemy chastotno-fazovoi avtopodstroiki chastoty”, Vestn. RAEN. Differ. uravn., 15:3 (2015), 97–102

[6] Mamonov S. S., Kharlamova A. O., “Kvazisinkhronnye rezhimy fazovoi sistemy”, Vestn. Ryazan. gos. radiotekhn. un-ta, 56 (2016), 45–51

[7] Mamonov S. S., Kharlamova A. O., “Predelnye tsikly pervogo roda fazovykh sistem”, Vestn. RAEN. Differ. uravn., 16:3 (2016), 68–74

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