On the existence and uniqueness of limit cycles for hybrid oscillators

被引：5
作者：
Chen, Hebai [1 ]
Xiao, Dongmei [2 ]
机构：
[1] Cent South Univ, Sch Math & Stat, HNP LAMA, Changsha 410083, Hunan, Peoples R China
[2] Shanghai Jiao Tong Univ, Sch Math Sci, CAM Shanghai, Shanghai 200240, Peoples R China
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2023年 / 202卷 / 05期
基金：
中国国家自然科学基金; 上海市自然科学基金;
关键词：
Limit cycle; Uniqueness; Existence; Criteria; Hybrid oscillator; NONEXISTENCE; VAN;
D O I：
10.1007/s10231-023-01312-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we first give criteria on the existence and uniqueness of limit cycles for x spexpressioncing diexpressioneresis + f (x, x)x + g(x) = 0, which is widely used to model the hybrid mechanical oscillators such as Van der Pol-Duffing-Rayleigh oscillator, Van der Pol-Rayleigh oscillator and so on. By applying the criteria, we completely prove the uniqueness of limit cycles for Van der Pol-Duffing-Rayleigh oscillator and an asymmetric and nonsmooth Van der Pol-Rayleigh oscillator. Moreover, we provide the location of the limit cycle when it exists.
引用
收藏
页码：2049 / 2071
页数：23
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