HOPF BIFURCATIONS IN NONAUTONOMOUS SYSTEMS AT POINTS OF RESONANCE

被引：0
|
作者：
程崇庆
机构：
[1] Nanjing University
[2] Department of Astronomy
来源：
Science China Mathematics | 1990年 / 02期
关键词：
Hcpf bifurcation; normal form; resonance;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Hopf bifurcations in periodically time-dependent systems are studied at points of resonance. By a new normal form, it is proved that the Poincare map has an invariant cycle emerging from the origin for some degenerate bifurcations. While for nondegenerate bifurcations, of primary interest is the case of 1:4 resonance, the existence and uniqueness of invariant cycle are proved when there is no nonzero fixed point.
引用
收藏
页码：206 / 219
页数：14
相关论文
共 50 条
  • [21] Discretizing dynamical systems with generalized Hopf bifurcations
    Paez Chavez, Joseph
    [J]. NUMERISCHE MATHEMATIK, 2011, 118 (02) : 229 - 246
  • [22] Discretizing dynamical systems with generalized Hopf bifurcations
    Joseph Páez Chávez
    [J]. Numerische Mathematik, 2011, 118 : 229 - 246
  • [23] HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
    Han, Maoan
    Yang, Junmin
    Yu, Pei
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2009, 19 (12): : 4117 - 4130
  • [24] DEGENERATE HOPF BIFURCATIONS IN POWER-SYSTEMS
    CHEN, RL
    VARAIYA, PP
    [J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (07): : 818 - 824
  • [25] Hopf bifurcations in general systems of Brusselator type
    Li, Yan
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2016, 28 : 32 - 47
  • [26] Strong Resonances at Hopf Bifurcations in Control Systems
    P.-A. Bliman
    A. M. Krasnosel'skii
    D. I. Rachinskii
    [J]. Automation and Remote Control, 2001, 62 : 1783 - 1802
  • [27] Nilpotent Hopf bifurcations in coupled cell systems
    Elmhirst, Toby
    Golubitsky, Martin
    [J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2006, 5 (02): : 205 - 251
  • [28] Strong resonances at Hopf bifurcations in control systems
    Bliman, PA
    Krasnosel'skii, AM
    Rachinskii, DI
    [J]. AUTOMATION AND REMOTE CONTROL, 2001, 62 (11) : 1783 - 1802
  • [29] Degenerate Hopf bifurcations in discontinuous planar systems
    Coll, B
    Gasull, A
    Prohens, R
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 253 (02) : 671 - 690
  • [30] Double singularity-induced bifurcation points and singular Hopf bifurcations
    Beardmore, RE
    [J]. DYNAMICS AND STABILITY OF SYSTEMS, 2000, 15 (04): : 319 - 342
12345