Surprisingly common outliers of a distribution tail, known as Dragon Kings, are seen in many complex systems. It has been argued that the general conditions for Dragon Kings in self-organized systems are high system coupling and low heterogeneity. In this Letter, we introduce a novel mechanism of Dragon Kings by discussing two closely-related stylized models of cascading failures. Although the first variant (based on simple contagion spreading and inoculation) exhibits well-studied self-organized criticality, the second one (based on both simple and complex contagion spreading) creates self-organized Dragon Kings in the failure size distribution. Next, we begin to understand the mechanistic origin of these Dragon Kings by mapping the probability of an initial cascade to a generalized birthday problem, which helps demonstrate that the Dragon King cascade is due to initial failures whose size exceeds a threshold that is infinitesimal compared to the size of the network. We use this finding to predict the onset of Dragon Kings with high accuracy using only logistic regression. Finally, we devise a simple control strategy that can decrease the frequency of Dragon Kings by orders of magnitude. We conclude with remarks on the applicability of both models to natural and engineered systems.
The Self-Organization of Dragon Kings
Yuansheng Lin, Keith Burghardt, Martin Rohden, Pierre-André Noël, Raissa M. D’Souza