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

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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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     author = {S. S. Mamonov and A. O. Kharlamova},
     title = {Cycles of the {First} {Kind} of {Systems} with {Cylindrical} {Phase} {Space}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
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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/