Critical behaviors of cascading dynamics on multiplex two-dimensional lattices

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 ( $${\textrm{CA}}$$ ) and deactivations ( $${\textrm{CD}}$$ ). We found that the giant viable clusters identified by $${\textrm{CA}}$$ and $${\textrm{CD}}$$ processes exhibit different critical behaviors. Specifically, the critical phenomena of $${\textrm{CA}}$$ processes are consistent with the ordinary bond percolation on a single layer but $${\textrm{CD}}$$ processes exhibit the critical behaviors consistent with mutual percolation on multiplex lattices. In addition, we computed the susceptibility of cascading dynamics using the concept of ghost field. Our results suggest that the $${\textrm{CA}}$$ and $${\textrm{CD}}$$ processes generate viable clusters in different ways.