Clustering of extreme events in complex systems

Understanding extreme, catastrophic events in Nature has a great significance in many situations including earthquakes, hurricanes, big storms, economic crisis, and so on. All these situations involve hazard and risk assessment with a great economic impact. A simplistic and practical approach to modeling extreme events in natural systems typically is to assume that extreme events are not correlated. In this noncorrelated case, there are mathematical results in the form of limit theorems that tell us the form of the extreme distribution depending on the parent distribution. However, there are strong indications that the hypothesis of lack of correlations between extreme events. Just think of earthquake precursors and replicas that clearly show strong temporal clustering of large events. In this contribution we investigate the existence of long-range temporal correlations in time series coming from deterministic but complex systems. By means of extensive computer simulations we investigate chaotic systems and the effect of coupling and system size on these correlations between large events.