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. 2012 Mar;38(2):293-303.
doi: 10.1007/s10867-011-9248-2. Epub 2011 Dec 10.

A distance-based dynamical transition analysis of time series signals and application to biological systems

Serkan Alagoz  1 , Baris Baykant Alagoz
Affiliations

A distance-based dynamical transition analysis of time series signals and application to biological systems

Serkan Alagoz et al. J Biol Phys. 2012 Mar.

Abstract

This study demonstrates an application of distance-based numerical measures to the phase space of time series signals, in order to obtain a temporal analysis of complex dynamical systems. This method is capable of detecting alterations appearing in the characters of the deterministic dynamical systems and provides a simple tool for the real-time analysis of time series data obtained from a complex dynamical system even with black box functionality. The study presents a possible application of the method in the dynamical transition analysis of real EEG records from epilepsy patients.

Keywords: Chaos; Dynamical system analysis; Epilepsy seizure prediction from EEG signal.

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Figures

Fig. 1
Fig. 1
a Illustration of trajectory curvatures in two-dimensional state space formula image. b Trajectory 1 is an escaping type trajectory with DE = 0.36, VE = 0.0028 and DEN = 128.67. Trajectory 2 is a slightly enwrapping type trajectory with DE = 0.31, VE = 0.0028 and DEN = 109.84. Trajectory 3 is an enwrapping type trajectory with DE = 0.23, VE = 0.0053 and DEN = 43.51 (length of trajectory and size of time window (w = 500) are equal)
Fig. 2
Fig. 2
a An orbit in the state space and distance vectors for states on a trajectory. b A representation of the complex dynamical system and the corresponding phase space formula image from time-delayed samples of the time series signal u(n)
Fig. 3
Fig. 3
Logarithmic STAD in a, logarithmic STV in b and NAD in c for the logistic difference equation with the parameters of A(0) = 0.1 and various values of r. Response of methods to stepwise temporal variation in the values of r in d (other parameters are w = 500, formula image = 3, p = 100, window sampling period Ts = 300)
Fig. 4
Fig. 4
a Sum of the single-channel EEG records from patient A. b WV of cumulative EEG in a. c STAD in logarithmic scale. d STV in logarithmic scale. e NAD (parameter settings: w = 10000, formula image = 1, p = 1000)
Fig. 5
Fig. 5
a Sum of the single-channel EEG records from patient B. b WV of cumulative EEG in a.c STAD in logarithmic scale. d STV in logarithmic scale. e NAD (parameter Settings: w = 10000, formula image = 1, p = 1000)
Fig. 6
Fig. 6
Logarithmic STAD, logarithmic STV, NAD, and 10×WV are plotted versus various SNR levels of noise. STAD, STV, and NAD are more robust against noise than WV
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