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
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