Equivariance identification using delay differential equations

The construction of delay differential equations (DDE) from recorded data h as been shown to be relevant to time series analysis. In particular, it all ows one to detect the presence of a deterministic component in the signal. Also, it provides an opportunity to generate classification schemes in whic h a given signal may be mapped onto an equivalence class. In this Letter, t his technique is applied to the important problem of symmetry detection in time series. Testing 24 numerical and 2 experimental time series, it is dem onstrated that DDEs allow one to quantify distinction between equivariant a nd invariant time series. (C) 2000 Published by Elsevier Science B.V. All r ights reserved.