Detecting determinism and nonlinear properties from empirical time series is highly nontrivial.
Traditionally, nonlinear time series analysis is based on an error-prone phase space reconstruction
that is only applicable for stationary, largely noise-free data from a low-dimensional system and
requires the nontrivial adjustment of various parameters. We present a data driven index based on
Fourier phases that detects determinism at a well deﬁned signiﬁcance level, without using Fourier
transform surrogate data. It extracts nonlinear features, is robust to noise, provides time-frequency
resolution by a double running window approach and potentially distinguishes regular and chaotic
dynamics. We test this method on data derived from dynamical models as well as on real world
data, namely intracranial recordings of an epileptic patient and a series of density related variations
of sediments of a paleolake in Tlaxcala, Mexico.
Presential in the seminar room. Zoom link:
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