Controllability of complex networks
Controllability of complex networks
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DOI：
10.1038/nature10011
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发表时间：
2011-05-12
期刊：
影响因子：
64.8
通讯作者：
Barabasi, Albert-Laszlo
中科院分区：
文献类型：
--
作者：
Liu, Yang-Yu;Slotine, Jean-Jacques;Barabasi, Albert-Laszlo
我们对自然或技术系统的理解的最终证明反映在我们控制它们的能力上。尽管控制理论为转向工程和自然系统提供了数学工具，但缺乏控制复杂的自组织系统的框架。在这里，我们开发了分析工具来研究任意复杂的有向网络的可控性，并通过时间相关控制识别驱动程序节点的集合，可以指导系统的整个动态。我们将这些工具应用于多个真实网络，发现驱动程序节点的数量主要取决于网络的分布。我们表明，在许多实际复杂系统中出现的稀疏不均匀网络是最难控制的，但是可以使用一些驱动程序节点来控制该密集和均匀的网络。违反直觉，我们发现在模型和实际系统中，驱动器节点倾向于避免高度节点。
The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network's degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.