Prediction and Suppression of Dragon Kings

A wide range of dynamical systems exhibit extreme events and critical transitions. The extent of damage and destruction these high-profile events may leave behind indicates the importance of the task of predicting them. We introduce a novel, unifying approach towards prediction of critical transitions. We explore rare events in the form of "Dragon Kings", unique, dramatic events that live beyond the distribution of other event sizes. We employ a network of synchronized

coupled chaotic circuits to demonstrate how loss of transverse stability in certain "hot spots" in the phase space of a dynamical system leads to occurrence of an extreme event. To this end we use covariant Lyapunov vectors as intrinsic directions of stability. We show how changes in the alignment between these vectors indicates a loss of stability that leads to an extreme event. We then empoly changes in the principal direction of these vectors to effectively forecast an upcoming

extreme event.