DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP

被引：3
|
作者：
Liu, Xingbo [1 ]
Liu, Junying [1 ]
Zhu, Deming [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 05期
关键词：
Bifurcation; heterodimensional cycle; orbit flip; local coordinates; HOMOCLINIC ORBITS; UNFOLDINGS;
D O I：
10.1142/S0218127413500806
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, nongeneric bifurcation analysis near heterodimensional cycles with orbit flip is investigated for three-dimensional systems. With the aid of a suitable local coordinate system, the Poincare map is constructed. By means of the bifurcation equations, the existence, nonexistence, coexistence and uniqueness of homoclinic orbit, periodic orbits and the heterodimensional cycle are studied, the relevant bifurcation surfaces and their existing regions are given. Some known results are extended. An example is given to show the existence of the system which has a heterodimensional cycle with orbit flip.
引用
收藏
页数：18
相关论文
共 50 条
  • [21] Dynamics Near the Heterodimensional Cycles with Nonhyperbolic Equilibrium
    Liu Xingbo
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (01):
  • [22] Codimension 3 non-resonant bifurcations of rough heteroclinic loops with one orbit flip
    Shuliang Shui
    Deming Zhu
    CHINESE ANNALS OF MATHEMATICS SERIES B, 2006, 27 (06) : 657 - 674
  • [23] Nongeneric bifurcations near a nontransversal heterodimensional cycle
    Xingbo Liu
    Xiaofei Wang
    Ting Wang
    Chinese Annals of Mathematics, Series B, 2018, 39 : 111 - 128
  • [24] Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip*
    Shuliang Shui
    Deming Zhu
    Chinese Annals of Mathematics, Series B, 2006, 27 : 657 - 674
  • [25] Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip
    Shuliang SHUI Deming ZHU College of Mathematics
    College of Sciences
    ChineseAnnalsofMathematics(SeriesB), 2006, (06) : 657 - 674
  • [26] BIFURCATION OF A HETERODIMENSIONAL CYCLE WITH WEAK INCLINATION FLIP
    Qiao, Zhiqin
    Zhu, Deming
    Lu, Qiuying
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2012, 17 (03): : 1009 - 1025
  • [27] Non-trivial wandering domains for heterodimensional cycles
    Kiriki, Shin
    Nakano, Yushi
    Soma, Teruhiko
    NONLINEARITY, 2017, 30 (08) : 3255 - 3270
  • [28] Homoclinic tangencies leading to robust heterodimensional cycles
    Barrientos, Pablo G.
    Diaz, Lorenzo J.
    Perez, Sebastian A.
    MATHEMATISCHE ZEITSCHRIFT, 2022, 302 (01) : 519 - 558
  • [29] Heterodimensional cycle bifurcation with two orbit flips
    Xingbo Liu
    Yancong Xu
    Sisi Wang
    Nonlinear Dynamics, 2015, 79 : 2787 - 2804
  • [30] Homoclinic tangencies leading to robust heterodimensional cycles
    Pablo G. Barrientos
    Lorenzo J. Díaz
    Sebastián A. Pérez
    Mathematische Zeitschrift, 2022, 302 : 519 - 558
12345