LIMIT CYCLES IN A SWITCHING LIENARD SYSTEM

被引：0
|
作者：
Wang, Xiangyu [1 ]
Guo, Laigang [2 ]
机构：
[1] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China
[2] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, MOE, Beijing 100875, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2023年 / 28卷 / 02期
关键词：
Lienard system; switching lines; Lyapunov constant; center; limit cycle;
D O I：
10.3934/dcdsb.2022132
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
ABSTRACT. In this paper, we consider a class of quadratic switching Lie ' nard systems with three switching lines. We give an algorithm for computing the Lyapunov constants of this system. Based on this method, we obtain a center condition and three limit cycles bifurcating from the focus (0, 0). Further, an example of quadratic switching systems is constructed to show the existence of six limit cycles bifurcating from the center. This is a new low bound on the maximal number of small-amplitude limit cycles obtained in such quadratic switching systems.
引用
收藏
页码：1503 / 1512
页数：10
相关论文
共 50 条
  • [31] THE NUMBER OF LIMIT CYCLES IN A Z2-EQUIVARIANT LIENARD SYSTEM
    Xiong, Yanqin
    Zhong, Hui
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (05):
  • [32] On the Distribution of Limit Cycles in a Lienard System with a Nilpotent Center and a Nilpotent Saddle
    Asheghi, R.
    Bakhshalizadeh, A.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (02):
  • [33] Nine Limit Cycles in a 5-Degree Polynomials Lienard System
    Cai, Junning
    Wei, Minzhi
    Zhu, Hongying
    COMPLEXITY, 2020, 2020
  • [34] ON THE NUMBER OF LIMIT CYCLES FOR A QUINTIC LIENARD SYSTEM UNDER POLYNOMIAL PERTURBATIONS
    Li, Linlin
    Yang, Junmin
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (06): : 2464 - 2481
  • [35] On the Number of Hyperelliptic Limit Cycles of Lienard Systems
    Qian, Xinjie
    Yang, Jiazhong
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2020, 19 (01)
  • [36] Fixed and moving limit cycles for Lienard equations
    Gasull, Armengol
    Sabatini, Marco
    ANNALI DI MATEMATICA PURA ED APPLICATA, 2019, 198 (06) : 1985 - 2006
  • [37] Maximum amplitude of limit cycles in Lienard systems
    Turner, N.
    McClintock, P. V. E.
    Stefanovska, A.
    PHYSICAL REVIEW E, 2015, 91 (01)
  • [38] Limit cycles of some polynomial Lienard systems
    Xu, Weijiao
    Li, Cuiping
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (01) : 367 - 378
  • [39] Limit cycles in discontinuous classical Lienard equations
    Martins, Ricardo Miranda
    Mereu, Ana Cristina
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2014, 20 : 67 - 73
  • [40] Limit Cycles of a Class of Cubic Lienard Equations
    Jin, Huatao
    Shui, Shuliang
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2011, 10 (02) : 317 - 326
12345