  Many real world complex systems such as infrastructure, communication and
transportation networks are embedded in space, where entities of one system may
depend on entities of other systems. These systems are subject to
geographically localized failures due to malicious attacks or natural
disasters. Here we study the resilience of a system composed of two
interdependent 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 its
complete collapse. If the attack is below the critical size, it will remain
localized. In contrast, under random attack a finite fraction of the system
needs to be removed to initiate system collapse. We present both numerical
simulations and a theoretical approach to analyze and predict the effect of
local attacks and the critical attack size. Our results demonstrate the high
risk of local attacks on interdependent spatially embedded infrastructures and
can be useful for designing more resilient systems.
