Received: 08 Sep 2001 © Copyright 2001
Accepted: Pending – 1 – http://www.csu.edu.au/ci/sub09/das01/
http://www.csu.edu.au/ci/
Draft Manuscript
Please note that this manuscript has yet to be accepted by Complexity International
Applicability of Lyapunov
Exponent in EEG data analysis
Atin Das, Pritha Das, A. B. Roy
Department of Mathematics, Jadavpur University,
Jadavpur, Calcutta 700 032, India
Email: atin_das@yahoo.com
Abstract
Importance of role of chaos in brain functioning has lead theoretical modelling as well as
analysis of electroencephalogram [EEG] data. Two most important chaotic measures are Lyapunov
exponent (LE) and dimensional analysis. But the reliability of LE in EEG data analysis has come
under question on the basis of the finding that EEG does not represent low dimensional chaos.
Here we address this question. We shall at first calculate LE and fractal dimension of EEG data
and known Lorenz system. We shall use the surrogating data method to remove nonlinearity of the
two datasets. A comparison of values of both the measures for original and its surrogated
counterpart is made to find if they can reflect the loss of nonlinearity and hence the loss of
information. We find that for EEG data, LE values does not reflect such change, but fractal
dimension shows such loss of information. In case of Lorenz data, both the measures reflect the
change correctly. So it can be concluded that LEs are not reliable tool in not low dimensional EEG
analysis.
1. Introduction
Electroencephalogram [EEG] represents the time series that maps the voltage corresponding
to neurological activity as a function of time. EEG is an observable property of large fields of
real neurons. Since the 1980s, when EEG signals could easily be connected to computers, the
technology has become widely used in mapping the brain. The status of EEG, despite for time
being eclipsed by that of single neuron recording, has since become a classic area of
investigating dynamics at the neurosystem level.
Many investigators, for example, Duke et al (1991), has proved that complex dynamical
evolutions lead to chaotic regimes. In the last thirty years, experimental observations have
pointed out that, in fact, chaotic systems are common in nature. A detail of such system is
given in Boccaletti et al. (2000).