Spatially localized attacks on interdependent networks: the existence of a finite critical attack size

TL;DR

This paper investigates how localized geographical attacks can cause widespread collapse in interdependent spatial networks, revealing a finite critical attack size that determines whether damage remains localized or spreads system-wide.

Contribution

It introduces a theoretical framework and simulations to identify the critical attack size for localized failures in interdependent spatial networks, highlighting their vulnerability.

Findings

Localized attacks above a finite size cause system-wide collapse.

Random attacks require removing a finite fraction of the system to cause collapse.

Theoretical predictions match numerical simulation results.

Abstract

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.