Siegert & Kantz "Prediction of Complex Dynamics - Who Cares About Chaos?"

Siegert, S., & Kantz, H. (2016). Prediction of Complex Dynamics: Who Cares About Chaos?. In Chaos Detection and Predictability (pp. 249-269). Springer, Berlin, Heidelberg.


We compile knowledge on limitations to prediction of the time evolution of complex systems. Although such systems are typically highly chaotic, the inverse of the maximal Lyapunov exponent, the Lyapunov time, is not the time scale beyond which predictions fail. Instead, as the example of weather forecasting will show, predictions can be successful on lead times which are several orders of magnitude longer. We analyze the reasons which prevent errors from growing exponentially fast with a rate related to the maximal Lyapunov exponent. Moreover, we advocate that standard practices from weather forecasting should be transferred to other fields of complex systems’ predictions, which includes a statement about the uncertainty related to the actual prediction and a performance measure on past predictions so that a decision maker can assess the potential quality of a forecasting scheme.