When Symmetrization Guarantees Synchronization in Directed Networks
When Symmetrization Guarantees Synchronization in Directed Networks
复制标题
当对称化保证有向网络中的同步时
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
V. Belykh
中科院分区：
文献类型：
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作者：
I. Belykh;M. Hasler;V. Belykh
我们回顾并说明了最近关于有向振子网络全局稳定同步的研究结果。考虑具有节点平衡的非对称连接网络，即指向某一节点的所有边的耦合系数之和等于从该节点向外的所有边的耦合系数之和。我们表明，对于这种有向但节点平衡的网络，用一半耦合强度的双向耦合取代单向耦合就足以使所有连接对称。然后，对称网络的同步条件保证了原有向网络的同步。以耦合驱动摆为例，给出了在具体的单向网络中如何证明同步的全局稳定性。我们还讨论了局部同步和全局同步的关系。
We review and illustrate our recent results on globally stable synchronization in directed oscillator networks. We consider asymmetrically connected networks with node balance, the property that the sum of the coupling coefficients of all edges directed to a node equals the sum of the coupling coefficients of all the edges directed outward from the node. We show that for such directed but node balanced networks, it is sufficient to symmetrize all connections by replacing a unidirectional coupling with a bidirectional coupling of half the coupling strength. The synchronization condition for the symmetrized network then guarantees synchronization in the original directed network. By considering an example of coupled driven pendula, we show how to prove global stability of synchronization in a concrete unidirectional network. We also discuss the relation between local and global synchronization.