Reduced order models for the prediction of the time of occurrence of extreme episodes

We describe in this paper a very special class of complex systems, namely those which admit reduced order models for the prediction of the peaks of a relevant variable (the output variable of the system). In particular, we show that if the attractor of the system is a torus or a low-dimensional strange attractor, such reduced order models exist and allow one to forecast the time of occurrence of the next peak, given the times of occurrence of the last three peaks. This property is particularly useful for forecasting recurrent extreme episodes in ecosystems.