Comparative study of nonlinear properties of EEG signals of a normal person and an epileptic patient

Background: Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent. Results: Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak \textit{et al.} [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases. Conclusions: In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation.Comment: Keywords:EEG, epilepsy, Correlation dimension, Surrogate analysis, Hurst exponent. 9 page

Frequency and wavelet based analyses of partial and complete measure synchronization in a system of three nonlinearly coupled oscillators

Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regime is sought from the power spectral analysis. The existence of PMS is confirmed using the order parameter M (here M-alpha beta for different combination pairs of oscillators), best suited to identify MS in coupled two-oscillator systems, and this definition is extended to obtain a new order parameter, M-3, aiding to distinguish complete MS of three oscillators from other forms of motion. The study of wavelet coefficient spectra sheds new light on the relative phase information of the oscillators in the QP PMS regions, also highlighting the intertwined role played by the various frequency components and their amplitudes as they vary temporally. Furthermore, this technique helps to draw a sharp distinction between CMS and chaotic unsynchronized states. Based on the Continuous Wavelet Transform coefficients of the three oscillators, an order parameter M-wav is defined to indicate the extent of synchronization of the various scales (frequencies) for different coupling strengths in the chaotic regime. Published by AIP Publishing