Identification determinism in time series based on symplectic geometry spectra

A new method based upon combination symplectic geometry spectra (SGS) with surrogate data analysis is proposed to identify its deterministic chaoticity or the stochastic nature from a scalar time series. Compared with the singular value decomposition (SVD), symplectic similar transform is nonlinear and has measure preserving characteristic, so the SGS can keep the essential character of the original time series. The power of the proposed algorithm to differentiate between deterministic, especially high-dimensional deterministic, and stochastic dynamics is tested on several numerically generated time series.