Self-organization of dragon king failures.

The mechanisms underlying cascading failures are often modeled via the paradigm of self-organized criticality. Here we introduce a simple network model where nodes self-organize to be either weakly or strongly protected against failure in a manner that captures the trade-off between degradation and reinforcement of nodes inherent in many network systems. If strong nodes cannot fail, any failure is contained to a single, isolated cluster of weak nodes and the model produces power-law distributions of failure sizes. We classify the large, rare events that involve the failure of only a single cluster as "black swans." In contrast, if strong nodes fail once a sufficient fraction of their neighbors fail, then failure can cascade across multiple clusters of weak nodes. If over 99.9% of the nodes fail due to this cluster hopping mechanism, we classify this as a "dragon king," which are massive failures caused by mechanisms distinct from smaller failures. The dragon kings observed are self-organized, existing over a wide range of reinforcement rates and system sizes. We find that once an initial cluster of failing weak nodes is above a critical size, 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 that can dramatically reduce dragon kings and other large failures.

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