Table Of ContentErol Ba§ar (Ed.)
Chaos
in
Brain Function
Containing Original Chapters by E. Basar and
T. H. Bullock and Topical Articles Repr'inted
from the Springer Series in Brain Dynamics
With 66 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo Hong Kong
Professor Dr. EROL BA~AR
Institute of Physiology
Medical University Lubeck
Ratzeburger Allee 160
D-2400 Lubeck 1, FRG
ISBN-13: 978-3-540-52329-1 e-ISBN-13: 978-3-642-75545-3
DOl: 10.1007/978-3-642-75545-3
Library of Congress Cataloging-in-Publication Data. Chaos in brain function/Erol Bapr, ed.
p. cm. "Containing original chapters by E. Ba~ar and T. H. Bullock and topical articles
reprinted from the Springer series in brain dynamics." Includes bibliographical references.
ISBN 0-387-52329-4 (U.S.: alk. paper) 1. Brain Mathematical models. 2. Chaotic behavior in
systems. I. Ba~ar, Ero!. II. Bullock, Theodore Holmes. III. Springer series in brain dynamics.
QP376.C47 1990 596'.0188-dc20 90-9560
This work is subject to copyright. All rights are reserved, whether the whole or part of the
material is concerned, specifically the rights of translation, reprinting, re-use of illustrations,
recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks.
Duplication of this publication or parts thereof is only permitted under the provisions of the
German Copyright Law of September 9, 1965, in its current version, and a copyright fee must
always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1990
Softcover reprint of the hardcover 18t edition 1990
The use of registered names, trademarks, etc. in this publication does not imply, even in the
absence of a specific statement, that such names are exempt from the relevant protective laws
and regulations and therefore free for general use.
Product liability: The publisher can give no guarantee for information about drug dosage and
application thereof contained in this book. In every individual case the respective user must
check its accuracy by consulting other pharmaceutical literature.
Typesetting, printing and bookbinding: Briihlsche Universitiitsdruckerei Giessen
2125/3130-543210 - Printed on acid-free paper
Preface
The analysis of deterministic chaos is currently an active field in many
branches of research. Mathematically all nonlinear dynamical systems
with more than two degrees of freedom can generate chaos, becoming
unpredictable over a longer time scale. The brain is a nonlinear system
par excellence. Accordingly, the concepts of chaotic dynamics have
found, in the last five years, an important application in research on
compound electrical activity of the brain. The present volume seeks to
cover most of the relevant studies in the newly emerging field of chaotic
attractors in the brain.
This volume is essentially a selection and reorganization of contri
butions from the first two volumes in the Springer Series in Brain
Dynamics, which were based on conferences held in 1985 and 1987
in Berlin. It also includes (a) a survey of progress in the recording of
evoked oscillations of the brain both at the cellular and EEG levels and
(b) an agenda for research on chaotic dynamics.
Although the first publications pointing out evidence of chaotic
behavior of the EEG did not appear until the beginning of 1985, the
presence of the pioneering scientists in this field gave the participants
at the first conference (volume 1) a strong impulse toward this field.
For me, as conference organizer, having been for a long time active in
nonlinear EEG research, the integration of this topic was self-evident;
however, the enthusiasm of the conference participants was greater
than expected.
Just two years later, there were three times as many contributions
to the second volume of Brain Dynamics, and the analysis of chaotic
attractors belonged to the important building blocks. Here the topic
"integrative functions of the brain" was dealt with in terms of several
multidisciplinary approaches. The response to the conference was so
favorable that two additional papers were added to volume 2, and the
authors were highly cooperative in making revisions in and additions
to their papers. The authors seemed not to be put off by the strong
review procedure but rather to be motivated by it. One of the editors
of volume 2, T. H. Bullock, insisted on methodological extensions and
conceptual additions on the basis of extensive interaction with the
authors' and postconference communication among experts.
The stimulus to publish this supplementary volume lay in the inter
est expressed by several persons to learn about and to start research
in this new field. At present it is still not easy to glean the relevant
publications, distributed over several special journals and conference
VI Preface
volumes. For this reason, the editor and the publisher decided that
a book of about 170 pages might more easily reach scientists working
in this new field than the two full volumes covering a much broader
spectrum of neuroscience.
Now greater than ever, we need new windows that can add to
the growing list of techniques for comprehension of electromagnetic
activity and local signs of change in the brain. In the "Epilogue" to
Brain Dynamics volume 2 Bullock points out the importance of the new
window as follows: "The contributions of Babloyantz, Rossler, Ba~ar
and Roschke, Skinner, Mpitsos, and others make me hopeful that we
will soon see the dimensionality of many parts of the brain at the same
time, second by second, in cats, catfish, and octopus, as rest changes
into arousal, directed attention and recognition." In fact, shortly there
after it became possible to realize some of these wishes. It is my
hope that this book as well will prove to address the genuine research
questions of the future.
The editor wishes to express his sincere thanks to Professor
T. H. Bullock for providing his constructive critique on the preliminary
survey and for adding his agenda for research on chaotic dynamics to
the present volume.
EROL BA~AR
Contents
Chaotic Dynamics and Resonance Phenomena
in Brain Function: Progress, Perspectives and Thoughts
E. BA~AR (With 6 Figures). . . . . . . . . . 1
An Agenda for Research on Chaotic Dynamics
T. H. BULLOCK. . . . . . . . . . . . . . . 31
Chaotic Dynamics in Brain Activity
A. BABLOYANTZ (With 3 Figures) .. 42
The EEG is Not a Simple Noise: Strange Attractors
in Intracranial Structures
J. RaSCHKE and E. BA~AR (With 7 Figures) . 49
Nonlinear Neural Dynamics in Olfaction
as a Model for Cognition
W. J. FREEMAN (With 3 Figures) 63
Self-Similarity in Hyperchaotic Data
O. E. ROSSLER and J. L. HUDSON (With 4 Figures) . 74
Estimation of Correlation Dimensions
from Single and Multichannel Recordings - A Critical View
A. BABLOYANTZ (With 4 Figures) . . . . . . . . . . . . 83
Correlation Dimensions in Various Parts of Cat
and Human Brain in Different States
J. RaSCHKE and E. BA~AR (With 14 Figures) . . 92
Magnetoencephalography and Attractor Dimension:
Normal Subjects and Epileptic Patients
K. SAERMARK, J. LEBECH, C. K. BAK, and A. SABERS
(With 7 Figures) . . . . . . . . . . . . . . .... 110
Chaotic Attractors in a Model of Neocortex:
Dimensionalities of Olfactory Bulb Surface Potentials
Are Spatially Uniform and Event Related
J. E. SKINNER, J. L. MARTIN, C. E. LANDISMAN, M. M. MOMMER,
K. FULTON, M. MITRA, W. D. BURTON, and B. SALTZBERG
(With 7 Figures) . . . . . . . . . . . . . . ....... 119
VIII Contents
Dimensional Analysis of the Waking EEG
K. E. GRAF and T. ELBERT (With 7 Figures) . . . . . . . . . 135
Analysis of Strange Attractors in EEGs
with Kinesthetic Experience and 4-D Computer Graphics
W. J. FREEMAN (With 4 Figures) . . . . . . . . . .. . 153
Chaos in Brain Function and the Problem of Nonstationarity:
A Commentary
G. J. MpITSOS . . . . . . . . . . . . . . . . . . . . . . 162
List of Contributors
BABLOYANTZ, A., Department of Physical Chemistry II,
Free University of Brussels, P.O. Box 231, Boulevard du Triomphe,
B-1050 Brussels, Belgium
BAK, C. K., Physics Laboratory I, Technical University of Denmark,
DK-2800 Lyngby, Denmark
BA~AR, E., Institute of Physiology, Medical University Lubeck,
Ratzeburger Allee 160, D-2400 Lubeck, FRO
BULLOCK, T. H., Department of Neurosciences A-001,
School of Medicine, University of California, San Diego, La Jolla,
CA 92093, USA
BURTON, W. D., Neurosciences Signal Analysis Laboratory,
Department of Psychiatry and Behavioral Science,
University of Texas Medical School, Houston, TX 77030, USA
ELBERT, T., Psychiatry, 116A3, Veterans Administration Medical Center,
3801 Miranda, Palo Alto, CA 94304, USA
FREEMAN, W. J., Department of Physiology-Anatomy,
University of California, Berkeley, CA 94720, USA
FULTON, K., Neurophysiology Section, Department of Neurology
and Neuroscience Program, Baylor College of Medicine,
Houston, TX 77030, USA
ORAF, K. E., Department of Clinical and Physiological Psychology,
University of Tubingen, Oartenstr. 29, D-7400 Tubingen, FRO
HUDSON, J. L., Department of Chemical Engineering,
University of Virginia, Charlottesville, VA 22901, USA
LANDISMAN, C. E., Neurophysiology Section, Department of Neurology
and Neuroscience Program, 'Baylor College of Medicine,
Houston, TX 77030, USA
LEBECH, J., Physics Laboratory I, Technical University of Denmark,
DK-2800 Lyngby, Denmark
MARTIN, J. L., Neurophysiology Section, Department of Neurology
and Neuroscience Program, Baylor College of Medicine,
Houston, TX 77030, USA
x List of Contributors
MITRA, M., Neurophysiology Section, Department of Neurology
and Neuroscience Program, Baylor College of Medicine,
Houston, TX 77030, USA
MOMMER, M. M., Neurophysiology Section, Department of Neurology
and Neuroscience Program, Baylor College of Medicine,
Houston, TX 77030, USA
MpITsos, G. J., M.O. Hatfield Marine Science Center,
Oregon State University, Newport, OR 97365, USA
RaSCHKE, J., Institute of Physiology, Medical University Lubeck,
Ratzeburger Allee 160, D-2400 Lubeck; FRG
ROSSLER, O. E., Institute of Physical and Theoretical Chemistry,
University of Tubingen, Auf der Morgenstelle 8,
D-7400 Tubingen, FRG
SABERS, A., Department of Neurology, Hvidovre Hospital,
DK-2650 Hvidovre, Denmark
SAERMARK, K., Physics Laboratory I, Technical University
of Denmark, DK-2800 Lyngby, Denmark
SALTZBERG, B., Neuroscience Signal Analysis Laboratory,
Department of Psychiatry and Behavioral Science,
University of Texas Medical School, Houston, TX 77030, USA
SKINNER, J. E., Neurophysiology Section, Department of Neurology
and Neuroscience Program, Baylor College of Medicine,
Houston, TX 77030, USA
Chaotic Dynamics and Resonance Phenomena
in Brain Function:
Progress, Perspectives, and Thoughts
E. BA~AR
1 Preliminary Remarks
My main goal by writing this survey is to try to bridge our knowledge in chaos
research with analysis of brain oscillatory phenomena both at the neuronal and
the EEG level.
In the years following the first measurement of human EEG by Hans Berger
and important developments by Lord Adrian and later Grey Walter, the pure
EEG research remained somewhat in the shadow of new discoveries based on
single-neuron recordings. From the beginning of 1960s the use of signal averagers
enabled EEG research scientists to extract the evoked potentials from the so
called random-noise EEG. In this context, the event-related potentials that con
tributed highly to the understanding of cognitive functions and to clinical diag
nostics were considered as deterministic signals whereas EEG was considered
mostly as pure noise.
In 1980 I stated strongly that we must not always consider the spontaneous
oscillations in brain electrical activity as a background noise. On the contrary, in
my own approach on field potentials, I assumed that the EEG must be con
sidered as one of the most important oscillations affecting the production and
conduction of signaling in the brain (Ba~ar 1980). This view was based on experi
ments with compound potentials from the cat and human brain. In this approach
some EEG fragments were considered as internal evoked potentials coming from
yet unknown or hidden sources. Further, evoked potentials were considered as
forced (or evoked) oscillations following known and deterministic inputs. Later,
I tentatively assumed that the EEG has a strange attractor (Ba~ar 1983 a, b). Ac
cording to these earlier steps and thoughts in considering the EEG as a
quasi deterministic signal, I brought experts together at conferences in 1983, 1985,
and 1987.
The most important development in the field of chaotic dynamics is to me,
without any question, the discovery by Babloyantz et al. (1985) who showed the
strange attract or behavior of EEG during the slow-wave sleep (SWS) stage. In
the same year we were able to show similar results from intracranial structures of
the cat brain; Rapp and coworkers published results on chaotic dynamics in the
same year (Raschke and Ba~ar 1985; Rapp et al. 1985 a, b).
With these introductory remarks I emphasize that the slogan "The EEG is not
noise, but is a quasideterministic signal" came from a need for interpreting results
of experiments by many neurophysiologists. The new development in research of
"chaos in brain function" is fascinating. However, this field cannot be considered
as an isolated research field. In the period of 1985-1989 during which chaotic
EEG results were substantially developed other noteworthy progress in the study
