[Paper Review] Predictability and control of extreme events in complex systems

Hugo L. D. de S. Cavalcante, Marcos Oriá+2 more|arXiv (Cornell University)|Jan 2, 2013

Complex Systems and Time Series Analysis5 citations

TL;DR

This paper identifies a distinct mechanism underlying extreme events in coupled chaotic oscillators that deviates from power-law statistics, enabling real-time forecasting of rare, large events. By detecting early warning signals, the study demonstrates that tiny, targeted perturbations can suppress these extreme events, offering a control strategy for complex systems prone to catastrophic dynamics.

ABSTRACT

In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme events. The mechanism responsible for the rare, largest events makes them distinct and their distribution deviates from a power-law. Based on this mechanism identification, we show that it is possible to forecast in real time an impending extreme event. Once forecasted, we also show that extreme events can be suppressed by applying tiny perturbations to the system.

Motivation & Objective

• To investigate the statistical properties of extreme events in coupled chaotic oscillators and challenge the assumption that they follow power-law distributions.
• To identify the underlying dynamical mechanism responsible for rare, large events that deviates from scale-free behavior.
• To develop a real-time forecasting method based on early warning signals of impending extreme events.
• To design and test a control strategy using minimal perturbations to suppress extreme events once forecasted.

Proposed method

• Analyzing coupled chaotic oscillators to observe the emergence of extreme events and their statistical distribution.
• Identifying a unique dynamical mechanism—distinct from power-law scaling—that governs the occurrence of the largest events.
• Detecting early warning signals in the system's state evolution preceding extreme events, enabling real-time prediction.
• Applying small, targeted perturbations to the system at the moment of forecast to suppress the development of extreme events.
• Using numerical simulations to validate the predictability and controllability of extreme events under the proposed framework.

Experimental results

Research questions

• RQ1 What statistical distribution governs extreme events in coupled chaotic oscillators, and does it deviate from power-law scaling?
• RQ2 What dynamical mechanism underlies the occurrence of the largest, rarest events in such systems?
• RQ3 Can early warning signals be reliably detected to forecast extreme events in real time?
• RQ4 Can minimal perturbations effectively suppress extreme events once they are predicted?

Key findings

• Extreme events in the studied coupled chaotic oscillators do not follow a power-law distribution, indicating a distinct underlying mechanism.
• The mechanism responsible for extreme events is characterized by specific dynamical precursors that can be detected in real time.
• Early warning signals allow for reliable forecasting of impending extreme events before their occurrence.
• Application of small, targeted perturbations at the forecast time successfully suppresses the development of extreme events.