Cascading failures in interdependent networks with finite functional components

摘要

We present a cascading failure model of two interdependent networks in whichfunctional nodes belong to components of size greater than or equal to $s$. Wefind theoretically and via simulation that in complex networks with randomdependency links the transition is first-order for $s\geq 3$ and second-orderfor $s=2$. We find for two square lattices with a distance constraint $r$ inthe dependency links that increasing $r$ moves the system from a regime withouta phase transition to one with a second-order transition. As $r$ continues toincrease the system collapses in a first-order transition. Each regime isassociated with a different structure of domain formation of functional nodes.