Localized attacks on spatially embedded networks with dependencies.

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.