On periodic solutions of Rayleigh equation

被引：1
|
作者：
Tlyachev, V. B. [1 ]
Ushkho, A. D. [1 ]
Ushkho, D. S. [1 ]
机构：
[1] Adyghe State Univ, 208 Pervomayskaya St, Maykop 385000, Russia
来源：
IZVESTIYA OF SARATOV UNIVERSITY MATHEMATICS MECHANICS INFORMATICS | 2021年 / 21卷 / 02期
关键词：
Poincare; Rayleigh equation; van der Pol equation; limit cycle; existence; uniqueness; EXISTENCE;
D O I：
10.18500/1816-9791-2021-21-2-173-181
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：173 / 181
页数：9
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