Dragon-king extreme events as precursors for catastrophic transition

Unexpected catastrophic transitions are often observed in complex systems. However, the prediction of such transitions is difficult in practice. Here, we find a special kind of extreme events with a dragon-king probability distribution that occur just prior to a catastrophic transition and, hence, can serve as its precursor. To illustrate the application of dragon kings as a precursor, we consider a practical experimental thermo-fluid system and a theoretical model of coupled logistic maps with quasi-periodic forcing, both systems displaying a catastrophic transition.