Geodesic
On periodic solutions of Rayleigh equation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 21 (2021) no. 2, pp. 173-181

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New sufficient conditions for the existence and uniqueness of a periodic solution of a system of differential equations equivalent to the Rayleigh equation are obtained. In contrast to the known results, the existence proof of at least one limit cycle of the system is based on applying curves of the topographic Poincare system. The uniqueness of the limit cycle surrounding a complex unstable focus is proved by the Otrokov method. 
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     author = {V. B. Tlyachev and A. D. Ushkho and D. S. Ushkho},
     title = {On periodic solutions of {Rayleigh} equation},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {173--181},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2021_21_2_a3/}
}
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V. B. Tlyachev; A. D. Ushkho; D. S. Ushkho. On periodic solutions of Rayleigh equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 21 (2021) no. 2, pp. 173-181. http://geodesic.mathdoc.fr/item/ISU_2021_21_2_a3/