Complexity measure of extreme events

Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of entropy and disequilibrium measures, separately or in combination. Chaotic signal was given prime importance in such studies while no such measure was proposed so far, how complex were the extreme events when compared to non-extreme chaos. We address here this question of complexity in extreme events and investigate if we can distinguish them from non-extreme chaotic signal. The normalized Shannon entropy in combination with disequilibrium is used for our study and it is able to distinguish between extreme chaos and non-extreme chaos and moreover, it depicts the transition points from periodic to extremes via Pomeau-Manneville intermittency and, from small amplitude to large amplitude chaos and its transition to extremes via interior crisis. We report a general trend of complexity against a system parameter that increases during a transition to extreme events, reaches a maximum, and then starts decreasing. We employ three models, a nonautonomous Liénard system, two-dimensional Ikeda map and a six-dimensional coupled Hindmarsh-Rose system to validate our proposition.