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It has been shown that a permutation can uniquely identify the joint set of an initial condition and a non-autonomous external force realization added to the deterministic system in given time series data. We demonstrate that our results can be applied to time series forecasting as well as the estimation of common external forces. Thus, permutations provide a convenient description for a time series data set generated by non-autonomous dynamical systems.

Permutations uniquely identify states and unknown external forces in non-autonomous dynamical systems