Chaotic Time Series Analysis

Chaotic Time Series Analysis

Chaotic dynamical systems are ubiquitous in nature and most of them does not have an explicit dynamical equation and can be only understood through the available time series. We here briefly review the basic concepts of time series and its analytic tools, such as dimension, Lyapunov exponent, Hilbert transform, and attractor reconstruction. Then we discuss its applications in a few fields such ...

Recent Developments in Chaotic Time Series Analysis

In this paper, two issues are addressed: (1) the applicability of the delay-coordinate embedding method to transient chaotic time series analysis, and (2) the Hilbert transform methodology for chaotic signal processing. A common practice in chaotic time series analysis has been to reconstruct the phase space by utilizing the delay-coordinate embedding technique, and then to compute dynamical in...

Chaotic Time Series Analysis: Improving the Procedures

Detecting Huntington Patient Using Chaotic Features of Gait Time Series

Huntington's disease (HD) is a congenital, progressive, neurodegenerative disorder characterized by cognitive, motor, and psychological disorders. Clinical diagnosis of HD relies on the manifestation of movement abnormalities. In this study, we introduce a mathematical method for HD detection using step spacing. We used 16 walking signals as control and 20 walking signals as HD. We took a s...

Resampling Chaotic Time Series

A method for resampling time series generated by a deterministic chaotic data generating process (DGP) is proposed. Given an observed time series, this method potentially allows one to obtain an arbitrary number of time series of arbitrary length which can be considered as a product of the same unknown DGP. The notion of shadowing and brittleness of the pseudo-orbit proves to be particularly us...