The extreme vulnerability of interdependent spatially embedded networks
The extreme vulnerability of interdependent spatially embedded networks
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DOI：
10.1038/nphys2727
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发表时间：
2013-10-01
期刊：
影响因子：
19.6
通讯作者：
Havlin, Shlomo
中科院分区：
文献类型：
--
作者：
Bashan, Amir;Berezin, Yehiel;Havlin, Shlomo
最近的研究表明，在相互依赖的网络中，一个网络中的一个非常小的故障可能导致灾难性的后果。在相互依赖的节点的临界分数以上，即使是单个节点故障也可以引起级联故障，这可能会突然使系统碎片化，而在这个临界依赖性以下，几个节点的故障只会导致对系统的少量损坏。到目前为止，研究主要集中在没有空间限制的相互依赖的随机网络。然而，许多真实的系统，如电网和互联网，并不是随机的，而是空间嵌入的。在这里，我们分析和数值研究的稳定性的相互依存的空间嵌入式网络建模为格子网络。令人惊讶的是，我们发现，在晶格系统中，与非嵌入式系统相比，没有关键的依赖关系，任何一小部分相互依赖的节点都会导致突然崩溃。我们表明，这种非常弱耦合晶格的极端脆弱性是一个后果的临界指数描述一个单一的晶格的渗流过渡。
Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, whereas below this critical dependency a failure of a few nodes leads only to a small amount of damage to the system. So far, research has focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically study the stability of interdependent spatially embedded networks modelled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no critical dependency and any small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice.