Hopf Bifurcation and Hidden Attractors of a Delay-Coupled Duffing Oscillator

被引：6
|
作者：
Zhao, Huitao [1 ]
Lin, Yiping
Dai, Yunxian
机构：
[1] Zhoukou Normal Univ, Coll Math & Stat, Zhoukou 466001, Henan, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2015年 / 25卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Delay-coupled Duffing oscillator; Hopf bifurcation; hidden attractor; CHAOTIC SYSTEM; MULTISTABILITY; FLOWS; STABILITY;
D O I：
10.1142/S021812741550162X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, a delay-coupled Duffing equation is studied. By the characteristic roots technique, sufficient conditions are obtained for Hopf bifurcation occurrence. And the spatio-temporal patterns of the bifurcating periodic solutions are also obtained, some examples are given to demonstrate the theoretical analysis. Especially, the obtained numerical simulation results show that there are hidden attractors in this delayed system, which can coexist with stable equilibrium or stable bifurcating orbits.
引用
收藏
页数：10
相关论文
共 50 条
  • [1] Hopf Bifurcation in Two Groups of Delay-Coupled Kuramoto Oscillators
    Guo, Yuxiao
    Jiang, Weihua
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2015, 25 (10):
  • [2] Double Hopf bifurcation and quasi-periodic attractors in delay-coupled limit cycle oscillators
    Li, Yanqiu
    Jiang, Weihua
    Wang, Hongbin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 387 (02) : 1114 - 1126
  • [3] Dynamics at Infinity, Degenerate Hopf and Zero-Hopf Bifurcation for Kingni-Jafari System with Hidden Attractors
    Wei, Zhouchao
    Moroz, Irene
    Wang, Zhen
    Sprott, Julien Clinton
    Kapitaniak, Tomasz
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (07):
  • [4] Hidden Attractors and Dynamics of a General Autonomous van der Pol-Duffing Oscillator
    Zhao, Huitao
    Lin, Yiping
    Dai, Yunxian
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (06):
  • [5] Hopf bifurcation and spatio-temporal patterns in delay-coupled van der Pol oscillators
    Song, Yongli
    NONLINEAR DYNAMICS, 2011, 63 (1-2) : 223 - 237
  • [6] Stabilization of periodic orbits near a subcritical Hopf bifurcation in delay-coupled networks
    Choe, Chol-Ung
    Jang, Hyok
    Flunkert, Valentin
    Dahms, Thomas
    Hoevel, Philipp
    Schoell, Eckehard
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2013, 28 (01): : 15 - 33
  • [7] Stability and bifurcation analysis in the delay-coupled nonlinear oscillators
    Z. Dadi
    Z. Afsharnezhad
    N. Pariz
    Nonlinear Dynamics, 2012, 70 : 155 - 169
  • [8] Stability and bifurcation analysis in the delay-coupled nonlinear oscillators
    Dadi, Z.
    Afsharnezhad, Z.
    Pariz, N.
    NONLINEAR DYNAMICS, 2012, 70 (01) : 155 - 169
  • [9] Hopf bifurcation and spatio-temporal patterns in delay-coupled van der Pol oscillators
    Yongli Song
    Nonlinear Dynamics, 2011, 63 : 223 - 237
  • [10] Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
    Cai, Yuting
    Zhang, Chunrui
    NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2017, 22 (05): : 598 - 613
12345