Complexity measures: Characterization of transition to extreme events in dynamical systems

In this work, we focus on different statistical measures to uncover the complexity of extreme events in various nonlinear dynamical systems. Notably, the effectiveness of the variance-based measure, estimated from the mean recurrence time and entropy, reveals a clear distinction between extreme and non-extreme events. Additionally, the variance measure clearly highlights the critical transition point of unforeseen, rare, large-amplitude dynamics. Our investigation involved models from various disciplines, including the Brusselator chemical oscillator, CO2 laser, superconducting quantum interference devices, and a coupled neuron model. Deeper insights into the complexity of extreme events offer significant value for advancing early prediction methods.