Cascading failures in interdependent networks with finite functional components

TL;DR

This paper models cascading failures in interdependent networks considering nodes with components of size at least s, revealing how the nature of phase transitions depends on component size and dependency link distance.

Contribution

It introduces a new model incorporating finite component size in cascading failures and analyzes how dependency link constraints affect transition types.

Findings

First-order transition for s≥3 in complex networks with random dependencies.

Second-order transition for s=2 in similar networks.

Transition type changes with dependency link distance r in lattice networks.

Abstract

We present a cascading failure model of two interdependent networks in which functional nodes belong to components of size greater than or equal to $s$. We find theoretically and via simulation that in complex networks with random dependency links the transition is first-order for $s\geq 3$ and second-order for $s=2$. We find for two square lattices with a distance constraint $r$ in the dependency links that increasing $r$ moves the system from a regime without a phase transition to one with a second-order transition. As $r$ continues to increase the system collapses in a first-order transition. Each regime is associated with a different structure of domain formation of functional nodes.