# Spreading of localized attacks in spatial multiplex networks

## TL;DR

This paper investigates how localized attacks can cause cascading failures in spatial multiplex networks, revealing critical attack sizes, novel scaling behaviors, and complex failure cascades with implications for real-world infrastructure resilience.

## Contribution

It introduces a theory to predict critical attack sizes and uncovers new scaling laws and failure cascade behaviors in spatial multiplex networks under localized attacks.

## Key findings

- Localized attacks can trigger system-wide cascades beyond a critical size.
- A metastable region exists where attacks induce nucleation-like failures.
- Theoretical predictions match observed scaling behaviors and cascade patterns.

## Abstract

Many real-world multilayer systems such as critical infrastructure are interdependent and embedded in space with links of a characteristic length. They are also vulnerable to localized attacks or failures, such as terrorist attacks or natural catastrophes, which affect all nodes within a given radius. Here we study the effects of localized attacks on spatial multiplex networks of two layers. We find a metastable region where a localized attack larger than a critical size induces a nucleation transition as a cascade of failures spreads throughout the system, leading to its collapse. We develop a theory to predict the critical attack size and find that it exhibits novel scaling behavior. We further find that localized attacks in these multiplex systems can induce a previously unobserved combination of random and spatial cascades. Our results demonstrate important vulnerabilities in real-world interdependent networks and show new theoretical features of spatial networks.