Bifurcation of limit cycles from a heteroclinic loop with a cusp

被引：38
|
作者：
Sun, Xianbo [1 ]
Han, Maoan [1 ]
Yang, Junmin [2 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050016, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 09期
基金：
中国国家自然科学基金;
关键词：
Nilpotent cusp; Heteroclinic loop; Melnikov function; Limit cycle; Bifurcation; POLYNOMIAL VECTOR-FIELDS; SYSTEMS;
D O I：
10.1016/j.na.2011.01.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we study the expansion of the first Melnikov function of a near-Hamiltonian system near a heteroclinic loop with a cusp and a saddle or two cusps, obtaining formulas to compute the first coefficients of the expansion. Then we use the results to study the problem of limit cycle bifurcation for two polynomial systems. (c) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2948 / 2965
页数：18
相关论文
共 50 条
  • [31] On the number of limit cycles near a homoclinic loop with a nilpotent cusp of order m
    Xiong, Yanqin
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 380 : 146 - 180
  • [32] BIFURCATION OF ROUGH HETEROCLINIC LOOP WITH ORBIT FLIPS
    Liu, Xingbo
    Wang, Zhenzhen
    Zhu, Deming
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (11):
  • [33] Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation
    Fengjie Geng
    Yancong Xu
    [J]. Nonlinear Dynamics, 2012, 70 : 1645 - 1655
  • [34] Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation
    Geng, Fengjie
    Xu, Yancong
    [J]. NONLINEAR DYNAMICS, 2012, 70 (02) : 1645 - 1655
  • [35] Theory and application of a nongeneric heteroclinic loop bifurcation
    Chow, SN
    Deng, B
    Friedman, MJ
    [J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1999, 59 (04) : 1303 - 1321
  • [36] ON BIFURCATION OF LIMIT-CYCLES FROM CENTERS
    CHICONE, C
    [J]. LECTURE NOTES IN MATHEMATICS, 1990, 1455 : 20 - 43
  • [37] On the Number of Limit Cycles Bifurcated from a Near-Hamiltonian System with a Double Homoclinic Loop of Cuspidal Type Surrounded by a Heteroclinic Loop
    Moghimi, Pegah
    Asheghi, Rasoul
    Kazemi, Rasool
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (01):
  • [38] Limit Cycles Near Homoclinic and Heteroclinic Loops
    Maoan Han
    Junmin Yang
    Alexandrina–Alina Tarţa
    Yang Gao
    [J]. Journal of Dynamics and Differential Equations, 2008, 20 : 923 - 944
  • [39] Limit Cycles Near Homoclinic and Heteroclinic Loops
    Han, Maoan
    Yang, Junmin
    Tarta, Alexandrina -Alina
    Gao, Yang
    [J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2008, 20 (04) : 923 - 944
  • [40] HETEROCLINIC LIMIT CYCLES IN COMPETITIVE KOLMOGOROV SYSTEMS
    Hou, Zhanyuan
    Baigent, Stephen
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (09): : 4071 - 4093
12345