On pinning synchronization of complex dynamical networks
On pinning synchronization of complex dynamical networks
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DOI：
10.1016/j.automatica.2008.07.016
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Wenwu Yu;Guanrong Chen;Jinhu Lu
中科院分区：
文献类型：
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作者：
Wenwu Yu;Guanrong Chen;Jinhu Lu
在复杂网络的钉扎控制中存在一些基本而又具有挑战性的问题：(1)对于给定的复杂网络，可以选择什么样的钉扎方案来实现同步？(2)可以设计什么样的控制器来确保网络的同步？(3)在给定的复杂网络中，应该使用多大的耦合强度来实现同步？本文对这些技术问题进行了研究。令人惊讶的是，通过对耦合强度的自适应调节，发现在典型框架下的网络可以在任何线性反馈钉扎方案下实现同步。此外，还发现当耦合强度较小时，应先钉扎低阶数的节点，这与通常认为连接程度最高的节点应先钉扎相反。此外，有趣的是，在高维设置中给出的带有控制器的派生钉扎条件可以被简化为低维条件，而不涉及钉扎控制器。最后，给出了无标度网络的仿真实例，验证了理论结果。
There exist some fundamental and yet challenging problems in pinning control of complex networks: (1) What types of pinning schemes may be chosen for a given complex network to realize synchronization? (2) What kinds of controllers may be designed to ensure the network synchronization? (3) How large should the coupling strength be used in a given complex network to achieve synchronization? This paper addresses these technique questions. Surprisingly, it is found that a network under a typical framework can realize synchronization subject to any linear feedback pinning scheme by using adaptive tuning of the coupling strength. In addition, it is found that the nodes with low degrees should be pinned first when the coupling strength is small, which is contrary to the common view that the most-highly-connected nodes should be pinned first. Furthermore, it is interesting to find that the derived pinning condition with controllers given in a high-dimensional setting can be reduced to a low-dimensional condition without the pinning controllers involved. Finally, simulation examples of scale-free networks are given to verify the theoretical results.