Critical behaviors of cascading dynamics on multiplex two-dimensional lattices

TL;DR

This paper investigates the critical behaviors of cascading processes in multiplex 2D lattices, revealing distinct percolation phenomena for activation and deactivation cascades through numerical simulations.

Contribution

It introduces and compares two cascading algorithms, CA and CD, demonstrating their different critical behaviors and linking them to known percolation models.

Findings

CA aligns with ordinary bond percolation

CD aligns with mutual percolation

Susceptibility analysis using ghost field

Abstract

We study the critical phenomena of viable clusters in multiplex two-dimensional lattices using numerical simulations. We identify viable sites on multiplex lattices using two cascading algorithms: the cascade of activations (CA) and deactivations (CD). We found that the giant viable clusters identified by CA and CD processes exhibit different critical behaviors. Specifically, the critical phenomena of CA processes are consistent with the ordinary bond percolation on a single layer but CD processes exhibit the critical behaviors consistent with mutual percolation on multiplex lattices. In addition, we computed the susceptibility of cascading dynamics by using the concept of ghost field. Our results suggest that the CA and CD processes generate viable clusters in different ways.