Singularity Analysis on a Planar System with Multiple Delays
Singularity Analysis on a Planar System with Multiple Delays
复制标题
DOI：
10.1007/s10884-006-9063-9
复制
发表时间：
2007-06
影响因子：
1.3
通讯作者：
Yuan Yuan-Yuan;Junjie Wei
中科院分区：
文献类型：
--
作者：
Yuan Yuan-Yuan;Junjie Wei
研究了一类具有多时滞的平面模型。利用标准动力学结果、中心流形理论和时滞泛函微分方程的规范形方法研究了模型的奇异性和相应的分支。结果表明，对于任意时滞，系统都存在Bogdanov-Takens（BT）奇异性，同时存在一系列的分叉和Hopf分叉。分别给出了规范形在BT奇点、纯虚本征值奇点和零本征值奇点处的展开。数值模拟已被提供来说明理论预测。
A planar model with multiple delays is studied. The singularities of the model and the corresponding bifurcations are investigated by using the standard dynamical results, center manifold theory and normal form method of retarded functional differential equations. It is shown that Bogdanov–Takens (BT) singularity for any time delays, and a serious of pitchfork and Hopf bifurcation can co-existent. The versal unfoldings of the normal forms at the BT singularity and the singularity of a pure imaginary and a zero eigenvalue are given, respectively. Numerical simulations have been provided to illustrate the theoretical predictions.