Hopf Bifurcation Calculations in Delayed Systems with Translational Symmetry
Hopf Bifurcation Calculations in Delayed Systems with Translational Symmetry
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DOI：
10.1007/s00332-004-0625-4
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发表时间：
2004-12
影响因子：
3
通讯作者：
G. Orosz;G. Stépán
中科院分区：
文献类型：
--
作者：
G. Orosz;G. Stépán
研究了n个具有平移对称性的单时滞动力系统平衡点的Hopf分支。由于平移对称性，属于相应时滞微分方程组平衡点的雅可比矩阵总是有一个零本征值。该特征根不依赖于系统参数，而其它特征根可能满足Hopf分叉条件。给出了一种计算这种Hopf分支(包括中心流形约化)的算法。封闭形式的结果展示了一个简单的模型，汽车追随沿一个环。
The Hopf bifurcation of an equilibrium in dynamical systems consisting of n equations with a single time delay and translational symmetry is investigated. The Jacobian belonging to the equilibrium of the corresponding delay-differential equations always has a zero eigenvalue due to the translational symmetry. This eigenvalue does not depend on the system parameters, while other characteristic roots may satisfy the conditions of Hopf bifurcation. An algorithm for this Hopf bifurcation calculation (including the center-manifold reduction) is presented. The closed form results are demonstrated for a simple model of cars following each other along a ring.