Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Tlyachev V. B., Ushkho A. D., Ushkho D. S. On periodic solutions of Rayleigh equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 2, pp. 173-181. DOI: 10.18500/1816-9791-2021-21-2-173-181, EDN: DOOKWV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.05.2021
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Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
501.1
DOI: 
10.18500/1816-9791-2021-21-2-173-181
EDN: 
DOOKWV

On periodic solutions of Rayleigh equation

Autors: 
Tlyachev V. B., Caucasus Mathematical Center Adyghe State University
Ushkho A. D., Caucasus Mathematical Center Adyghe State University
Ushkho D. S., Caucasus Mathematical Center Adyghe State University
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
References: 
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Received: 
18.05.2020
Accepted: 
31.10.2020
Published: 
31.05.2021
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