Estimating complexity of spike-wave discharges with largest Lyapunov exponent in computational models and experimental data

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

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The Lyapunov Exponent Variance of an Electronic Manufacturing Enterprise’s Daily Qualified Rate Time Series by Improved Small Data Sets Approach

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.197.271 ◽

2012 ◽

Vol 197 ◽

pp. 271-277

Author(s):

Zhu Ping Gong

Keyword(s):

Time Series ◽

Lyapunov Exponent ◽

Chaotic Time Series ◽

Quality System ◽

Quality Level ◽

Largest Lyapunov Exponent ◽

Small Data ◽

Data Set ◽

Electronic Manufacturing ◽

Small Data Set

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.

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The zona incerta modulates spontaneous spike-wave discharges in the rat

Journal of Neurophysiology ◽

10.1152/jn.00750.2011 ◽

2013 ◽

Vol 109 (10) ◽

pp. 2505-2516 ◽

Cited By ~ 8

Author(s):

Fu-Zen Shaw ◽

Yi-Fang Liao ◽

Ruei-Feng Chen ◽

Yu-Hsing Huang ◽

Rick C. S. Lin

Keyword(s):

Functional Role ◽

Significant Inhibition ◽

Zona Incerta ◽

Obvious Effect ◽

Spike Wave Discharges ◽

Long Evans ◽

Oscillation Frequencies ◽

Spike Wave ◽

Stimulation Of

The contribution of the zona incerta (ZI) of the thalamus on spike-wave discharges (SWDs) was investigated. Chronic recordings of bilateral cortices, bilateral vibrissa muscle, and unilateral ZI were performed in Long-Evans rats to examine the functional role of SWDs. Rhythmic ZI activity appeared at the beginning of SWD and was accompanied by higher-oscillation frequencies and larger spike magnitudes. Bilateral lidocaine injections into the mystacial pads led to a decreased oscillation frequency of SWDs, but the phenomenon of ZI-related spike magnitude enhancement was preserved. Moreover, 800-Hz ZI microstimulation terminates most of the SWDs and whisker twitching (WT; >80%). In contrast, 200-Hz ZI microstimulation selectively stops WTs but not SWDs. Stimulation of the thalamic ventroposteriomedial nucleus showed no obvious effect on terminating SWDs. A unilateral ZI lesion resulted in a significant reduction of 7- to 12-Hz power of both the ipsilateral cortical and contralateral vibrissae muscle activities during SWDs. Intraincertal microinfusion of muscimol showed a significant inhibition on SWDs. Our present data suggest that the ZI actively modulates the SWD magnitude and WT behavior.

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Theoretical basis for the hypothesis of white-matter resonance as a background of spike-wave discharges

Physics in Medicine ◽

10.1016/j.phmed.2020.100031 ◽

2020 ◽

pp. 100031

Author(s):

Shigeki Sadahiro

Keyword(s):

White Matter ◽

Theoretical Basis ◽

Spike Wave Discharges ◽

Spike Wave

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Study of Rehabilitation of Injured Knee Joint Applying Chaotic Theory in Human Body Motion

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.342-343.581 ◽

2007 ◽

Vol 342-343 ◽

pp. 581-584

Author(s):

Byung Young Moon ◽

Kwon Son ◽

Jung Hong Park

Keyword(s):

Time Series ◽

Lyapunov Exponent ◽

Angular Displacement ◽

Three Dimensional ◽

Gait Pattern ◽

Body Motion ◽

Largest Lyapunov Exponent ◽

Chaos Analysis ◽

Nonlinear Technique ◽

Injured Knee

Gait analysis is essential to identify accurate cause and knee condition from patients who display abnormal walking. Traditional linear tools can, however, mask the true structure of motor variability, since biomechanical data from a few strides during the gait have limitation to understanding the system. Therefore, it is necessary to propose a more precise dynamic method. The chaos analysis, a nonlinear technique, focuses on understanding how variations in the gait pattern change over time. Healthy eight subjects walked on a treadmill for 100 seconds at 60 Hz. Three dimensional walking kinematic data were obtained using two cameras and KWON3D motion analyzer. The largest Lyapunov exponent from the measured knee angular displacement time series was calculated to quantify local stability. This study quantified the variability present in time series generated from gait parameter via chaos analysis. Gait pattern is found to be chaotic. The proposed Lyapunov exponent can be used in rehabilitation and diagnosis of recoverable patients.

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Detection of Epileptic Spike-Wave Discharges Using SVM

2007 IEEE International Conference on Control Applications ◽

10.1109/cca.2007.4389275 ◽

2007 ◽

Cited By ~ 5

Author(s):

Yaozhang Pan ◽

Shuzhi Sam Ge ◽

Feng Ru Tang ◽

Abdullah Al Mamun

Keyword(s):

Spike Wave Discharges ◽

Epileptic Spike ◽

Spike Wave

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A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416502266 ◽

2016 ◽

Vol 26 (13) ◽

pp. 1650226 ◽

Cited By ~ 20

Author(s):

Eduardo M. A. M. Mendes ◽

Erivelton G. Nepomuceno

Keyword(s):

Lyapunov Exponent ◽

Lower Bound ◽

Equations Of Motion ◽

Original System ◽

Glass System ◽

Largest Lyapunov Exponent ◽

Simple Method ◽

Interval Extensions

In this letter, a very simple method to calculate the positive Largest Lyapunov Exponent (LLE) based on the concept of interval extensions and using the original equations of motion is presented. The exponent is estimated from the slope of the line derived from the lower bound error when considering two interval extensions of the original system. It is shown that the algorithm is robust, fast and easy to implement and can be considered as alternative to other algorithms available in the literature. The method has been successfully tested in five well-known systems: Logistic, Hénon, Lorenz and Rössler equations and the Mackey–Glass system.

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