Synchronous Dynamics and Bifurcation Analysis in Two Delay Coupled Oscillators with Recurrent Inhibitory Loops

被引：3
|
作者：
Wang, Lianhua [1 ]
Peng, Jian [2 ]
Jin, Yiming [1 ]
Ma, Jianjun [1 ]
机构：
[1] Hunan Univ, Coll Civil Engn, Changsha 410082, Hunan, Peoples R China
[2] Hunan Univ, Coll Mech & Vehicle Engn, Changsha 410082, Hunan, Peoples R China
来源：
JOURNAL OF NONLINEAR SCIENCE | 2013年 / 23卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Synchronization; Delay; Bifurcation; Stability; Normal form; FUNCTIONAL-DIFFERENTIAL EQUATIONS; NEURAL OSCILLATORS; HOPF-BIFURCATION; CONNECTION; NEURONS;
D O I：
10.1007/s00332-012-9151-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this study, the dynamics and low-codimension bifurcation of the two delay coupled oscillators with recurrent inhibitory loops are investigated. We discuss the absolute synchronization character of the coupled oscillators. Then the characteristic equation of the linear system is examined, and the possible low-codimension bifurcations of the coupled oscillator system are studied by regarding eigenvalues of the connection matrix as bifurcation parameter, and the bifurcation diagram in the gamma-rho plane is obtained. Applying normal form theory and the center manifold theorem, the stability and direction of the codimension bifurcations are determined. Moreover, the symmetric bifurcation theory and representation theory of Lie groups are used to investigate the spatio-temporal patterns of the periodic oscillations. Finally, numerical results are applied to illustrate the results obtained.
引用
收藏
页码：283 / 302
页数：20
相关论文
共 50 条
  • [1] Synchronous Dynamics and Bifurcation Analysis in Two Delay Coupled Oscillators with Recurrent Inhibitory Loops
    Lianhua Wang
    Jian Peng
    Yiming Jin
    Jianjun Ma
    Journal of Nonlinear Science, 2013, 23 : 283 - 302
  • [2] Synchronous dynamics of two coupled oscillators with inhibitory-to-inhibitory connection
    Peng, Jian
    Guo, Shangjiang
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (12) : 4131 - 4148
  • [3] Synchronization for two coupled oscillators with inhibitory connection
    Xiao, Ke
    Guo, Shangjiang
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2010, 33 (07) : 892 - 903
  • [4] Hopf Bifurcation in Two Groups of Delay-Coupled Kuramoto Oscillators
    Guo, Yuxiao
    Jiang, Weihua
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2015, 25 (10):
  • [5] Bifurcation analysis of multistability of synchronous states in the system of two delay-coupled oscillators
    Adilova, A. B.
    Balakin, M. I.
    Gerasimova, S. A.
    Ryskin, N. M.
    CHAOS, 2021, 31 (11)
  • [6] Analysis of bifurcation in a symmetric system of m coupled oscillators with delay
    Zhang, Chunrui
    Zheng, Baodong
    APPLIED MATHEMATICAL MODELLING, 2014, 38 (19-20) : 4586 - 4601
  • [7] Simple bifurcation of coupled advertising oscillators with delay
    Zhang, Chunrui
    Yin, Haidong
    Zheng, Huifeng
    APPLIED MATHEMATICS LETTERS, 2011, 24 (11) : 1840 - 1844
  • [8] HOPF BIFURCATION OF A CLASS OF TWO COUPLED RELAXATION OSCILLATORS OF THE VAN DER POL TYPE WITH DELAY
    Wu, Xiaoqin P.
    Wang, Liancheng
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2010, 13 (02): : 503 - 516
  • [9] Stability and bifurcation analysis in the delay-coupled nonlinear oscillators
    Z. Dadi
    Z. Afsharnezhad
    N. Pariz
    Nonlinear Dynamics, 2012, 70 : 155 - 169
  • [10] Stability and bifurcation analysis in the delay-coupled nonlinear oscillators
    Dadi, Z.
    Afsharnezhad, Z.
    Pariz, N.
    NONLINEAR DYNAMICS, 2012, 70 (01) : 155 - 169
12345