Symmetry analysis of coupled scalar systems under time delay
Symmetry analysis of coupled scalar systems under time delay
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DOI：
10.1088/0951-7715/28/3/795
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发表时间：
2015-02
期刊：
影响因子：
1.7
通讯作者：
F. Atay;H. Ruan
中科院分区：
文献类型：
--
作者：
F. Atay;H. Ruan
研究了具有耦合时滞的一般网络结构中的耦合单元系统。我们证明了从平衡点开始的不稳定分叉是由网络耦合矩阵的极值特征值控制的。基于等变度方法及其计算程序包，我们对耦合单元双向环中的失稳分支进行了对称性分类。讨论了定常分叉和振荡分叉。我们还引入了次支配轨道类型的概念来捕捉次极大性质的分支解。
We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based on the equivariant degree method and its computational packages, we perform a symmetry classification of destabilizing bifurcations in bidirectional rings of coupled units. Both stationary and oscillatory bifurcations are discussed. We also introduce the concept of secondary dominating orbit types to capture bifurcating solutions of submaximal nature.