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 Izv. Saratov Univ. Math. Mech. Inform., 2021, Volume 21, Issue 2, Pages 173–181 (Mi isu884)

Scientific Part
Mathematics

On periodic solutions of Rayleigh equation

V. B. Tlyachev, A. D. Ushkho, D. S. Ushkho

Adyghe State University, 208 Pervomayskaya St., Maykop 385000, Russia

Abstract: 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.

Key words: Poincare, Rayleigh equation, van der Pol equation, limit cycle, existence, uniqueness.

DOI: https://doi.org/10.18500/1816-9791-2021-21-2-173-181

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Bibliographic databases:

UDC: 501.1
Revised: 31.10.2020

Citation: V. B. Tlyachev, A. D. Ushkho, D. S. Ushkho, “On periodic solutions of Rayleigh equation”, Izv. Saratov Univ. Math. Mech. Inform., 21:2 (2021), 173–181

Citation in format AMSBIB
\Bibitem{TlyUshUsh21} \by V.~B.~Tlyachev, A.~D.~Ushkho, D.~S.~Ushkho \paper On periodic solutions of Rayleigh equation \jour Izv. Saratov Univ. Math. Mech. Inform. \yr 2021 \vol 21 \issue 2 \pages 173--181 \mathnet{http://mi.mathnet.ru/isu884} \crossref{https://doi.org/10.18500/1816-9791-2021-21-2-173-181} \elib{https://elibrary.ru/item.asp?id=45797871}