On the number of limit cycles for a perturbed cubic reversible Hamiltonian system

被引：0
|
作者：
Yang, Jihua [1 ]
机构：
[1] Tianjin Normal Univ, Sch Math Sci, Tianjin 300387, Peoples R China
来源：
CHAOS | 2024年 / 34卷 / 10期
基金：
中国国家自然科学基金;
关键词：
ISOCHRONOUS CENTERS; PIECEWISE-SMOOTH; BIFURCATION; INTEGRALS; PLANAR;
D O I：
10.1063/5.0211447
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the limit cycle problem of a cubic reversible Hamiltonian system under perturbation of polynomials of degree n with a switching line x = 0. The upper and lower bounds of the number of limit cycles are obtained using the first order Melnikov function and its expansion. The method for calculating the Melnikov function relies upon some iterative formulas, which differs from other approaches.
引用
收藏
页数：9
相关论文
共 50 条
  • [21] Heteroclinic bifurcation of limit cycles in perturbed cubic Hamiltonian systems by higher-order analysis
    Geng, Wei
    Han, Maoan
    Tian, Yun
    Ke, Ai
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 357 : 412 - 435
  • [22] Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
    Zhang, TH
    Han, MA
    Zang, H
    Meng, XZ
    CHAOS SOLITONS & FRACTALS, 2004, 22 (05) : 1127 - 1138
  • [23] ON THE NUMBER OF LIMIT CYCLES OF A CUBIC SYSTEM NEAR A CUSPIDAL LOOP
    Yun Tian
    Annals of Applied Mathematics, 2010, 26 (02) : 222 - 226
  • [24] Numerical Investigation of Limit Cycles to A Non-Hamiltonian Perturbed Integrable System
    Hong, Xiaochun
    Hong, Lijun
    Wang, Bin
    2015 11TH INTERNATIONAL CONFERENCE ON NATURAL COMPUTATION (ICNC), 2015, : 583 - 587
  • [25] BIFURCATION OF LIMIT CYCLES FOR CUBIC REVERSIBLE SYSTEMS
    Shao, Yi
    Wu, Kuilin
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2014,
  • [26] BIFURCATIONS OF LIMIT CYCLES FOR A PERTURBED CUBIC SYSTEM WITH DOUBLE FIGURE EIGHT LOOP
    Zhang, Tonghua
    Zang, Hong
    Tade, Mose O.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (04):
  • [27] Limit cycles of a perturbed cubic polynomial differential center
    Buica, Adriana
    Llibre, Jaume
    CHAOS SOLITONS & FRACTALS, 2007, 32 (03) : 1059 - 1069
  • [28] On the number of limit cycles for perturbed pendulum equations
    Gasull, A.
    Geyer, A.
    Manosas, F.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (03) : 2141 - 2167
  • [29] Bifurcations of Limit Cycles in A Perturbed Quintic Hamiltonian System with Six Double Homoclinic Loops
    Yong-xi Gao Yu-hai Wu Li-xin Tian Department of Mathematics
    Acta Mathematicae Applicatae Sinica, 2008, (02) : 313 - 328
  • [30] Bifurcations of limit cycles in a perturbed quintic Hamiltonian system with six double homoclinic loops
    Yong-xi Gao
    Yu-hai Wu
    Li-xin Tian
    Acta Mathematicae Applicatae Sinica, English Series, 2008, 24 : 313 - 328
12345