Ordinal patterns for characterization of transition to extreme events

Ordinal patterns serve as a symbolic representation to explore the complex features of distinct nonlinear dynamical systems and real-world data. This work focuses on unveiling the effectiveness of ordinal pattern measures to illustrate the intricate processes associated with extreme events and other dynamics. We specifically illustrate three different types of large expansions: strange nonchaotic extreme events, rare events originating from chaotic motion, and hyperchaotic extreme events and their transitions. The well-known largest Lyapunov exponent method does not shows any unique features for different types of extreme events. However, the ordinal pattern-based permutation entropy measure distinguishes between extreme and non-extreme events across three different dynamic processes. The robustness of the ordinal pattern measure is also validated using noise-induced extreme events. Our investigation sheds light on uncovering the complexity of unforeseen large-amplitude events in a wide range of complex systems.