Many real world complex systems such as infrastructure, communication andtransportation networks are embedded in space, where entities of one system maydepend on entities of other systems. These systems are subject togeographically localized failures due to malicious attacks or naturaldisasters. Here we study the resilience of a system composed of twointerdependent spatially embedded networks to localized geographical attacks.We find that if an attack is larger than a finite (zero fraction of the system)critical size, it will spread through the entire system and lead to itscomplete collapse. If the attack is below the critical size, it will remainlocalized. In contrast, under random attack a finite fraction of the systemneeds to be removed to initiate system collapse. We present both numericalsimulations and a theoretical approach to analyze and predict the effect oflocal attacks and the critical attack size. Our results demonstrate the highrisk of local attacks on interdependent spatially embedded infrastructures andcan be useful for designing more resilient systems.
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