On the detection of determinism in a time series
The authors propose a simple and numerically robust method for differentiating chaotic dynamics from stochastic dynamics which is of special importance in the study of aperiodic and apparently irregular signals. This cannot be done by conventional spectral analysis since both chaos and random signals have continuous broadband power spectra. But as the nonlinear theory of dynamical systems shows, a chaotic process would have a finite dimensional attractor whereas a truly random process would be infinitely large dimensional. In order to work out the difference the nonlinear scaled distributions of the strengths of the orthogonal modes in the data of a time series are compared with the derivate from its surrogate counterpart. Relatively decreasing strengths of the weaker modes with increasing dimension of the orthogonal spaces mapping the process indicates chaoticity. The proposed method is based on singular value decomposition which is often used for the characterization of chaotic dynamics. In contrast to earlier works on the subject the sets of normalized orthogonal modes generated are mutually nonlinearly related and the energy distribution in each set of orthogonal modes of the data matrix is nonlinearly scaled.
scientific article; zbMATH DE number 1370241
scientific article