Journal of Physics A, Vol. 265(2000) 264-273

Equivariance identification using delay differential equations

C. Lainscsek¹, C. Letellier², J. Kadtke³, G. Gouesbet², F. Schürrer⁴

1	Cognitive Science Department; University of California at San Diego; 9500 Gilman Drive; La Jolla, CA 92093-0515; USA
2	CORIA UMR 6614, Université de Rouen; Place Emile Blondel; 76131 Mont Saint-Aignan Cedex; France
3	MPL, Scripps Institution of Oceanography; University of California at San Diego; 9500 Gilman Dr.; La Jolla, CA 92093-0238; USA
4	Institute for Theoretical Physics; Technical University of Graz; Petersgasse 16, A-8010 Graz; Austria

Abstract:

The construction of Delay Differential Equations (DDE) from recorded data has been shown to be relevant to time series analysis. In particular, it allows one to detect the presence of a deterministic component in the signal. Also, it provides an opportunity to generate classification schemes in which a given signal may be mapped onto an equivalence class. In this paper, this technique is applied to the important problem of symmetry detection in time series. Testing 24 numerical and 2 experimental time series, it is demonstrated that DDEs allow one to quantify distinction between equivariant and invariant time series.