On the existence of bifocal heteroclinic cycles in a class of four-dimensional piecewise affine systems

被引:8
作者
Wu, Tiantian [1 ]
Yang, Xiao-Song [1 ]
机构
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
基金
中国国家自然科学基金;
关键词
D O I
10.1063/1.4949474
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Based on mathematical analysis, this paper provides a methodology to ensure the existence of heteroclinic cycles in a class of four-dimensional piecewise affine systems. In addition, examples are provided to illustrate the effectiveness of the method. Published by AIP Publishing.
引用
收藏
页数:8
相关论文
共 18 条
  • [1] Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
    Ashwin, Peter
    Burylko, Eksandr
    Maistrenko, Yuri
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2008, 237 (04) : 454 - 466
  • [2] Rank one chaos in a class of planar systems with heteroclinic cycle
    Chen, Fengjuan
    Han, Maoan
    [J]. CHAOS, 2009, 19 (04)
  • [3] DiBernardo M, 2008, APPL MATH SCI, V163, P1, DOI 10.1007/978-1-84628-708-4
  • [4] Bifurcations of generic heteroclinic loop accompanied by transcritical bifurcation
    Geng, Fengjie
    Liu, Dan
    Zhu, Deming
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2008, 18 (04): : 1069 - 1083
  • [5] Singular heteroclinic cycles
    Homburg, AJ
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 161 (02) : 358 - 402
  • [6] Homoclinic snaking near a heteroclinic cycle in reversible systems
    Knobloch, J
    Wagenknecht, T
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2005, 206 (1-2) : 82 - 93
  • [7] Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
    Leonov, G. A.
    Kuznetsov, N. V.
    Mokaev, T. N.
    [J]. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2015, 224 (08) : 1421 - 1458
  • [8] Fishing principle for homoclinic and heteroclinic trajectories
    Leonov, G. A.
    [J]. NONLINEAR DYNAMICS, 2014, 78 (04) : 2751 - 2758
  • [9] EXACT HETEROCLINIC CYCLE FAMILY AND QUASI-PERIODIC SOLUTIONS FOR THE THREE-DIMENSIONAL SYSTEMS DETERMINED BY CHAZY CLASS IX
    Li, Jibin
    Zhao, Xiaohua
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2011, 21 (05): : 1357 - 1367
  • [10] Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system
    Messias, Marcelo
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (11)