Self-Organization of Dragon Kings

TL;DR

This paper introduces a model explaining how network systems can self-organize into states prone to rare, massive failures called Dragon Kings, highlighting the conditions and control strategies influencing their emergence.

Contribution

The study presents a novel model capturing the self-organization of nodes into weak or strong states, explaining the emergence of Dragon Kings and their dependence on initial failure sizes.

Findings

Dragon Kings occur when initial failures exceed a critical size.

The size of initial weak clusters predicts Dragon King likelihood.

Random upgrades can unintentionally increase system vulnerability.

Abstract

The mechanisms underlying cascading failures are often modeled via the paradigm of self-organized criticality. Here we introduce a simple model where nodes self-organize to be either weak or strong to failure which captures the trade-off between degradation and reinforcement of nodes inherent in many network systems. If strong nodes cannot fail, this leads to power law distributions of failure sizes with so-called "Black Swan" rare events. In contrast, if strong nodes fail once a sufficient fraction of their neighbors fail, this leads to "Dragon Kings", which are massive failures caused by mechanisms distinct from smaller failures. In our model, we find that once an initial failure size is above a critical value, the Dragon King mechanism kicks in, leading to piggybacking system-wide failures. We demonstrate that the size of the initial failed weak cluster predicts the likelihood of a Dragon King event with high accuracy and we develop a simple control strategy which also reveals that a random upgrade can inadvertently make the system more vulnerable. The Dragon Kings observed are self-organized, existing throughout the parameter regime.