Advanced chaos forecasting

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Abstract
The exponential separation of initially adjacent trajectories restricts the predictability of deterministic chaotic motions. The predictability depends on the initial state from where the trajectory starts that shall be forecasted. By calculating the predictability simultaneously with the forecast, we are able to reject forecasts with low reliability immediately, thereby decreasing drastically the average forecast error. We test this scheme experimentally on Chua’s circuit [Komuro, Tokunaga, Matsumoto, Chua, and Hotta, Int. J. Bifurc. Chaos 1, 139 (1991)], basing all calculations only on a time series of a single scalar variable.