Sandpiles on multiplex networks

TL;DR

This paper studies the sandpile model on multiplex networks, revealing that multiplexity preserves critical avalanche scaling but influences cascade dynamics, especially for hubs, highlighting the importance of multiplex modeling for real-world systems.

Contribution

It introduces the sandpile model on multiplex networks and shows how multiplexity affects cascade dynamics without changing the critical avalanche scaling behavior.

Findings

Avalanche size distribution follows a power-law with exponent 3/2.

Higher-degree nodes are more prone to failure in multiplex networks.

Multiplexity influences cascade dynamics but not the critical scaling law.

Abstract

We introduce the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche dynamics; the system is critical with an asymptotic power-law avalanche size distribution with an exponent $\tau = 3/2$ on duplex random networks. The detailed cascade dynamics, however, is affected by the multiplex coupling. For example, higher-degree nodes such as hubs in scale-free networks fail more often in the multiplex dynamics than in the simplex network counterpart in which different types of edges are simply aggregated. Our results suggest that multiplex modeling would be necessary in order to gain a better understanding of cascading failure phenomena of real-world multiplex complex systems, such as the global economic crisis.