Dragon kings in self-organized criticality systems

The spontaneous emergence of scale invariance, called self-organized criticality (SOC), is often attributed to a second-order absorbing-state phase transition (ASPT). Many real-world systems display SOC, yet with extreme events overrepresented, called dragon kings (DKs) and causing significant disruption. We show analytically that the trade-off between driving impulse and dissipation rate can create DKs in a second-order ASPT. This establishes that DKs exist in SOC systems, reveals a taxonomy of DKs, and shows that larger dissipation and smoother driving lower risk of extreme events.