Seven large-amplitude limit cycles in a cubic polynomial system

被引：13
|
作者：
Liu, YR [1 ]
Huang, WT
机构：
[1] Guilin Univ Elect Technol, Dept 7th, Guilin 541004, Peoples R China
[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2006年 / 16卷 / 02期
基金：
中国国家自然科学基金;
关键词：
focal value; singular point value; infinity; limit cycle; isochronous center;
D O I：
10.1142/S0218127406014940
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the problem of limit cycles bifurcated from the equator for a cubic polynomial system is investigated. The best result so far in the literature for this problem is six limit cycles. By using the method of singular point value, we prove that a cubic polynomial system can bifurcate seven limit cycles from the equator. We also find that a rational system has an isochronous center at the equator.
引用
收藏
页码：473 / 485
页数：13
相关论文
共 50 条
  • [1] A cubic polynomial system with seven limit cycles at infinity
    Zhang, Qi
    Liu, Yirong
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 177 (01) : 319 - 329
  • [2] SIXTEEN LARGE-AMPLITUDE LIMIT CYCLES IN A SEPTIC SYSTEM
    Zhang, Lina
    Li, Feng
    Alsaedi, Ahmed
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2018, 8 (06): : 1821 - 1832
  • [3] Large-amplitude limit cycles in resonantly coupled oscillators
    Ananthkrishnan, N
    Sudershan, S
    Sudhakar, K
    Verma, A
    [J]. JOURNAL OF SOUND AND VIBRATION, 2000, 231 (05) : 1377 - 1382
  • [4] Large-amplitude limit cycles via a homoclinic bifurcation mechanism
    Sharma, A
    Ananthkrishnan, N
    [J]. JOURNAL OF SOUND AND VIBRATION, 2000, 236 (04) : 725 - 729
  • [5] Small amplitude limit cycles for the polynomial Lienard system
    Borodzik, Maciej
    Zoladek, Henryk
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (09) : 2522 - 2533
  • [6] A cubic system with twelve small amplitude limit cycles
    Liu, YR
    Huang, WT
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2005, 129 (02): : 83 - 98
  • [7] Application of secondary bifurcations to large-amplitude limit cycles in mechanical systems
    Ananthkrishnan, N
    Sudhakar, K
    Sudershan, S
    Agarwal, A
    [J]. JOURNAL OF SOUND AND VIBRATION, 1998, 215 (01) : 183 - 188
  • [8] Center problem and the bifurcation of limit cycles for a cubic polynomial system
    Du, Chaoxiong
    Huang, Wentao
    Zhang, Qi
    [J]. APPLIED MATHEMATICAL MODELLING, 2015, 39 (17) : 5200 - 5215
  • [9] Cubic system with eight small-amplitude limit cycles
    James, E.M.
    Lloyd, N.G.
    [J]. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 1991, 47 (02): : 163 - 171
  • [10] The center conditions and bifurcation of limit cycles at the infinity for a cubic polynomial system
    Zhang, Lina
    Liu, Yirong
    Jiang, Xuejiao
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (04) : 1360 - 1370
12345