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Mon Jun 6 10:15:51 EDT 1988

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Comment on John Moody's remarks about chaos in neural systems

Today we have at our disposal a variety of methods to assess from an
experimental time series some of the dynamical properties of the system
under study.  These methods (phase space construction, Poincare maps,
correlation dimensions, Lyapunov exponents, Kolmogorov entropies, ...)
may give us a quantitative measure of the real brain activity.  In 1985,
these methods were used for the first time in the analysis of brain
activity [1] from the electroencephalogram (EEG) recordings.

Although the origin of the EEG is not well understood, however several well
defined stages of the brain activity show characteristic EEG's which are
still used as diagnostic tools.  We showed that several stages of the sleep
cycle could obey low dimensional chaotic dynamics.  Later, this kind of
analysis has been extended by other laboratories [2] and our group [3] to
the study of other stages of the brain activity.

The general conclusions are:
1) Eyes open, the brain activity shows noise-like behavior (very high
dimensional)
2) Eyes closed, the dynamics may be described by a chaotic attractor of
relatively low dimension (around 6)
3) This value decreases during the sleep cycle and reaches a minimum near 4
in the deep sleep (stage IV)
4) The REM (dream) episods are characterized by a rather high dimensional or
noise-like behavior
5) During severe pathologies such as epileptic seizures (petit mal) and coma
(terminal state of the Creutzfeld-Jakob disease), the correlation dimension
drops to lower values (2.05 for petit mal).

Therfore higher is the dimension, more alert is the brain.  Could chaos
be associated with processing power?  This goes in the same direction as
the findings of Golberger et al. [4] about dying heart that you mentioned.
We have found that the normal heart is not a periodic oscillator but the
variabilities between successive beats shows non random behavior [5].
Here again, the normal rule is a chaotic state whereas pathologies seem
to be associated with more coherent behavior.

Regarding the computing abilities of chaotic systems, there has been
a great deal of work done on these topics (see for ex. J.S. Nicolis in [6]).
With its particular properties, the chaotic attractor is an interesting
candidate for information processing:  it continuously creates and destroys
information (in the sense of Shannon) in the same time.  There is a
constant creation of new conditions (a large region of phase space
may be visited), while the memory of the present state is
progressively lost ...

Now, how to design a neural network which could take profit of
such properties is another question.  However, we think that still
much interesting work could be done in this direction.

We are presently engaged in such studies and we try to refine these data
with more accurate technics.

Anyone interested may write at:  R09614 at BBRBFU01.BITNET

Any comment is wellcome.

Alain Destexhe             Agnessa Babloyantz

Faculte des Sciences, Universite Libre de Bruxelles,
Campus de la Plaine (CP-231), Bd. du Triomphe,
B-1050 Brussels, Belgium

[1] A.Babloyantz, C.Nicolis & M.Salazar: Phys. Lett. 111A: 152 (1985)
[2] S.P.Layne, G.Mayer-Kress & J.Holzfuss: in Dimensions and Entropies in
     Chaotic Systems Ed G.Mayer-Kress (Springer Berlin 1986)
    I.Dvorak & J.Siska: Phys. lett. 118A: 63 (1986)
    P.E.Rapp, I.D.Zimmerman, A.M.Albano, G.C.de Guzman, N.N.Greenbaun &
     T.R.Bashore: in Nonlinear Oscillations in Biology and Chemistry Ed. H.G.
     Othmer Lectures notes in Biomathematics 66: 175 (Springer Berlin 1986)
    C.A.Skarda & W.J.Freeman: Behavior. Brain Sci. 10: 187 (1987)
    J.Roschke & E.Basar: in Dynamics of Sensory and Cognitive Processing by the
     Brain, Ed E.Basar, Springer Series in Brain Dynamics, Vol 1,  203 (1988)
[3] A. Babloyantz & A. Destexhe: in Temporal Disorder in Human Oscillatory
     Systems Eds. L. Rensing, U. an der Heiden and M.C. Mackey, Springer series
     in Synergetics 36:48 (1987a)
    A.Babloyantz & A.Destexhe: in Proceedings of the first IEEE International
     Conference on Neural Networks, Eds M. Caudill and C Butler Vol 4: 31(1987)
    A.Babloyantz & A.Destexhe: Proc. Natl. Acad. Sci. USA 83: 3513 (1986)
    A.Babloyantz & A.Destexhe: in From Chemical to Biological Organization,  Ed
     by M.Markus, S.Muller and G.Nicolis, Springer, Berlin (1988)
[4] A.Babloyantz & A.Destexhe: Biol. Cybernetics 58: 131 (1988)
[5] A.Goldberger, V.Barghava, B.J.West & A.J.Mandell: Physica 17D: 207 (1985)
[6] J.S.Nicolis: in Hierarchical systems, Springer, Berlin (1985)
    J.S.Nicolis, G.Mayer-Kress & G.Haubs: Z.Naturforsh. 38a: 1157 (1983)