Dynamics of cascades in spatial interdependent networks

TL;DR

This paper explores how the range of dependency interactions influences cascade dynamics in spatial interdependent networks, revealing various phase transitions and their underlying mechanisms, with implications for physical interdependent systems.

Contribution

It characterizes different phase transitions in spatial interdependent networks based on dependency range and links cascade behaviors to physical systems like superconductors.

Findings

Different types of phase transitions depend on dependency range.

Identification of mixed-order, first-order, and second-order transitions.

Prediction of a novel fourth transition type influenced by microscopic interventions.

Abstract

The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for increasing range of dependency couplings, different types of phase transition accompanied by various cascade kinetics can be observed including mixed-order transition characterized by critical branching phenomena, first-order transition with nucleation cascades, and continuous second-order transition with weak cascades. We also describe the dynamics of cascades at the mutual mixed-order resistive transition in interdependent superconductors and show its similarity to that of percolation of interdependent abstract networks. Finally, we layout our perspectives for the experimental observation of these phenomena, their phase diagrams and the underlying kinetics, in the context of physical interdependent networks. Our studies of interdependent networks shed light on the possible mechanisms of three known types of phase transitions, second order, first order, and mixed order as well as predicting a novel fourth type where a microscopic intervention will yield a macroscopic phase transition.