Berezin Yehiel, Bashan Amir, Danziger Michael M, Li Daqing, Havlin Shlomo
Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel.
Channing Division of Network Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA, USA.
Sci Rep. 2015 Mar 11;5:8934. doi: 10.1038/srep08934.
Many real world complex systems such as critical infrastructure networks are embedded in space and their components may depend on one another to function. They are also susceptible to geographically localized damage caused by malicious attacks or natural disasters. Here, we study a general model of spatially embedded networks with dependencies under localized attacks. We develop a theoretical and numerical approach to describe and predict the effects of localized attacks on spatially embedded systems with dependencies. Surprisingly, we find that a localized attack can cause substantially more damage than an equivalent random attack. Furthermore, we find that for a broad range of parameters, systems which appear stable are in fact metastable. Though robust to random failures-even of finite fraction-if subjected to a localized attack larger than a critical size which is independent of the system size (i.e., a zero fraction), a cascading failure emerges which leads to complete system collapse. Our results demonstrate the potential high risk of localized attacks on spatially embedded network systems with dependencies and may be useful for designing more resilient systems.
许多现实世界中的复杂系统，如关键基础设施网络，都嵌入在空间中，其组件可能相互依赖才能运行。它们还容易受到恶意攻击或自然灾害造成的地理局部性破坏。在此，我们研究一种在局部攻击下具有依赖性的空间嵌入网络的通用模型。我们开发了一种理论和数值方法来描述和预测局部攻击对具有依赖性的空间嵌入系统的影响。令人惊讶的是，我们发现局部攻击可能比同等的随机攻击造成大得多的破坏。此外，我们发现对于广泛的参数范围，看似稳定的系统实际上是亚稳的。尽管对随机故障具有鲁棒性——即使是有限比例的随机故障——但如果受到大于临界尺寸（该临界尺寸与系统大小无关，即零比例）的局部攻击，就会出现级联故障，导致系统完全崩溃。我们的结果证明了对具有依赖性的空间嵌入网络系统进行局部攻击可能存在的高风险，并且可能有助于设计更具弹性的系统。
