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
相关论文
共 23 条
  • [11] Highest weak focus order for trigonometric Lienard equations
    Gasull, Armengol
    Gine, Jaume
    Valls, Claudia
    [J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2020, 199 (04) : 1673 - 1684
  • [12] Fixed and moving limit cycles for Lienard equations
    Gasull, Armengol
    Sabatini, Marco
    [J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2019, 198 (06) : 1985 - 2006
  • [13] Hale J. K., 1980, ORDINARY DIFFERENTIA
  • [14] LARGE-AMPLITUDE PERIODIC OSCILLATIONS IN SUSPENSION BRIDGES - SOME NEW CONNECTIONS WITH NONLINEAR-ANALYSIS
    LAZER, AC
    MCKENNA, PJ
    [J]. SIAM REVIEW, 1990, 32 (04) : 537 - 578
  • [15] Levinson N., 1942, Duke Math. J, V9, P382, DOI [10.1215/S0012-7094-42-00928-1, DOI 10.1215/S0012-7094-42-00928-1]
  • [16] Massera JL., 1954, EUROSURVEILLANCE, V9, P367
  • [17] Asymmetric oscillators and twist mappings
    Ortega, R
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1996, 53 : 325 - 342
  • [18] Thomson W.T., 1998, Theory of vibration with applications
  • [19] On the uniqueness and nonexistence of limit cycles for predator-prey systems
    Xiao, DM
    Zhang, ZF
    [J]. NONLINEARITY, 2003, 16 (03) : 1185 - 1201
  • [20] Ye YanQian., 1986, Theory of limit cycles, volume 66 of Translations of Mathematical Monographs, Vsecond
123