Principles of Brain Functioning: A Synergetic Approach to Brain Activity, Behavior and Cognition

339 Pages·1996·11.58 MB·English

by  Professor Dr. Dr. h.c.mult. Hermann Haken (auth.)

Principles of Brain Functioning
Springer
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Springer Series in Synergetics
Editor: Hermann Haken
An ever increasing number of scientific disciplines deal with complex systems. These are systems that
are composed of many parts which interact with one another in a more or less complicated manner. One
of the most striking features of many such systems is their ability to spontaneously form spatial or
temporal structures. A great variety of these structures are found, in both the inanimate and the living
world. In the inanimate world of physics and chemistry, examples include the growth of crystals,
coherent oscillations oflaser light, and the spiral structures formed in fluids and chemical reactions. In
biology we encounter the growth of plants and animals (morphogenesis) and the evolution of species.
In medicine we observe, for instance, the electromagnetic activity of the brain with its pronounced
spatio-temporal structures. Psychology deals with characteristic features of human behavior ranging
from simple pattern recognition tasks to complex patterns of social behavior. Examples from sociology
include the formation of public opinion and cooperation or competition between social groups.
In recent decades, it has become increasingly evident that all these seemingly quite different kinds
of structure formation have a number ofi mportant features in common. The task of studying analogies
as well as differences between structure formation in these different fields has proved to be an ambitious
but highly rewarding endeavor. The Springer Series in Synergetics provides a forum for interdisciplinary
research and discussions on this fascinating new scientific challenge. It deals with both experimental and
theoretical aspects. The scientific community and the interested layman are becoming ever more
conscious ofc oncepts such as self-organization, instabilities, deterministic chaos, nonlinearity, dynamical
systems, stochastic processes, and complexity. All of these concepts are facets of a field that tackles
complex systems, namely synergetics. Students, research workers, university teachers, and interested
laymen can find the details and latest developments in the Springer Series in Synergetics, which
publishes textbooks, monographs and, occasionally, proceedings. As witnessed by the previously
published volumes, this series has always been at the forefront of modern research in the above
mentioned fields. It includes textbooks on all aspects of this rapidly growing field, books which provide
a sound basis for the study of complex systems.
A selection of volumes in the Springer Series in Synergetics: .
Synergetics An Introduction 3rd Edition 49 Neuronal Cooperativity
ByH. Haken Editor: J. Kriiger
5 Pattern Formation by Dynamic Systems 50 Synergetic Computers and Cognition
and Pattern Recognition A Top-Down Approach to Neural Nets
Editor: H. Haken ByH.Haken
20 Advanced Synergetics 2nd Edition
55 Rhythms in Physiological Systems
ByH.Haken
Editors: H. Haken, H. P. Koepchen
1.3 Synergetics of the Brain
58 Self-Organization and Clinical
Editors: E. Ba'far, H. Flohr, H. Haken,
Psychology Empirical Approaches
A. J. Mandell
to Synergetics in Psychology
31 Complex Systems - Operational
Editors: W. Tschacher, G. Schiepek,
Approaches in Neurobiology, Physics,
E.J. Brunner
and Computers Editor: H. Haken
62 Interdisciplinary Approaches
36 Temporal Disorder
to Nonlinear Complex Systems
in Human Oscillatory Systems
Editors: H. Haken, A. Mikhailov
Editors: 1. Rensing, U. an der Heiden,
M. C. Mackey 64 Ambiguity in Mind and Nature
38 Computational Systems -Natural and Multistable Cognitive Phenomena
Artificial Editor: H. Haken Editors: P. Kruse, M. Stadler
40 Information and Self-Organization 66 Self-Organization in Optical Systems and
A Macroscopic Approach to Complex Applications in Information Technology
Systems By H. Haken Editors: M. A. Vorontsov, W. B. Miller
42 Neural and Synergetic Computers 67 Principles of Brain Functioning
Editor: H. Haken A Synergetic Approach to Brain Activity,
45 Synergetics of Cognition Behavior and Cognition
Editors: H. Haken, M. Stadler ByH.Haken
Hermann Haken
Principles of
Brain Functioning
A Synergetic Approach to Brain Activity,
Behavior and Cognition
With 220 Figures
Springer
Professor Dr. Dr. h.c.mult. Hermann aaken
Institut fUr Theoretische Physik und Synergetik der Universitat Stuttgart
D-70550 Stuttgart, Germany and
Center for Complex Systems, Florida Atlantic University
Boca Raton, FL 33431, USA
Series Editor:
Professor Dr. Dr. h.c.mult. Hermann Haken
Institut fUr Theoretische Physik und Synergetik der Universitat Stuttgart
D-70550 Stuttgart, Germany and
Center for Complex Systems, Florida Atlantic University
Boca Raton, FL 33431, USA
LIbrary of Congress Cataloglng-In-Publlcatlon Data
Haken. H.
PrIncIples of braIn functIoning, a synergetlc approach to brain
activIty. behavlor. and cognition I Hermann Haken.
p. cm. -- (Springer serIes In synergetlcs ; 67)
Inc I udes bIb 1I ograph I ca I references.
ISBN-13: 978-3-642-79572-5 e-ISBN-13: 978-3-642-79578-1
001: 18.1887/ 978-3-642-79578-1
1. Braln--Mathematlcal models. 2. System theory. 1. TItle.
11. Ser I es, Spr I nger ser I es In synerget I cs ; v. 67.
[ONLM, 1. Bra I n-":phys I 0 I ogy. 2. Mode Is. Theoret Ica 1.
3. Movement--physlology. 4. Thlnklng--physlology. 5. VIsual
Percept I on--phys I 0 1o gy. 6. El ectroencepha 1o graphy. HL 300 HI55p
19961
OP376.H25 1996
612.S·2--dc20 95-41276
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for prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1996
Softcover reprint of the hardcover 1st edition 1996
The use of general descriptive names, 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
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Typesetting: Camera ready copy from the author using a Springer TEX macro package
SPIN 10493001 55/3144 -5 4 3 2 1 0 -Printed on acid-free paper
To my friends
Waltraut and Achim Finke
with deep gratitude
Preface
It is increasingly being recognized that the experimental and theoretical study
of the complex system brain requires the cooperation of many disciplines, in
cluding biology, medicine, physics, chemistry, mathematics, computer science,
linguistics, and others. In this way brain research has become a truly interdis
ciplinary endeavor. Indeed, the most important progress is quite often made
when different disciplines cooperate. Thus it becomes necessary for scientists
to look across the fence surrounding their disciplines. The present book is
written precisely in this spirit. It addresses graduate students, professors and
scientists in a variety of fields, such as biology, medicine and physics. Be
yond its mathematical representation the book gives ample space to verbal
and pictorial descriptions of the main and, as I believe, fundamental new
insights, so that it will be of interest to a general readership, too.
I use this opportunity to thank my former students, some of whom are
my present co-workers, for their cooperation over many years. Among them
I wish to mention in particular M. Bestehorn, L. Borland, H. Bunz, A. Daf
fertshofer, T. Ditzinger, E. Fischer, A. Fuchs, R. Haas, R. Honlinger, V. Jirsa,
M. Neufeld, M. Ossig, D. Reimann, M. Schanz, G. Schoner, P. Tass, C. Uhl.
My particular thanks go to R. Friedrich and A. Wunderlin for their constant
help in many respects. Stimulating discussions with a number of colleagues
from a variety of fields are also highly appreciated. At the risk of omitting
some important names, I wish to mention P. Kruse and M. Stadler on the
connections between Gestalt theory and synergetics, E. Ba§ar, T. Bullock,
W. Freeman, D. Lehmann, H. Petsche, and G. Pfurtscheller on various as
pects of EEG measurements and their interpretation, H. Korndle and K.H.
Leist for analysis of movements, especially on the pedalo device. My thanks
go further to P. Beek and W. Beek, o. Meijer, and L. Peper for discussions
on movement coordination and the role of order parameters, P. Vanger for
his cooperation on the recognition of facial expressions, and to J. Portugali
on his concept of interrelational networks. My special thanks go to my friend
and colleague Scott Kelso, who, in particular through his ingeniously devised
and accurate experiments, decisively contributed to the proof that the con
cepts of synergetics play a fundamental role in movement coordination and
related fields. I think it is fair to say that a paradigm shift has occurred here;
VIII Preface
namely, instead of studying stable states, we are now studying transitions
close to instability points, transitions that occur in our brain.
This book could have never been completed without the tireless help of
my secretary Mrs. 1. Maller, who typed several versions of this manuscript
including all its formulas and performed the miracle of combining great speed
with utmost accuracy. In addition, Mrs. Maller, together with my co-worker
R. Haas, brought the manuscript into its final form, ready for printing. A. Daf
fertshofer and further members of my institute carefully read the manuscript.
He, as well as R. Haas, V. Jirsa, D. Reimann and C. Uhl made valuable sug
gestions. The figures were prepared by A. Daffertshofer and M. Neufeld. I
thank all of them for their great help.
Last but not least I thank the members of the Springer-Verlag for the
traditionally excellent cooperation, in particular Prof. W. Beiglback, Dr. A.
Lahee, and Ms. Petra Treiber.
Stuttgart, October 1995 Hermann Haken
Table of Contents
Prologue...................................................... 1
Part I Foundations ........................................... 5
1. Introduction.............................................. 7
1.1 Biological Systems Are Complex Systems. . . . . . . . . . . . . . . . . . 7
1.2 Goals of Synergetics .................. . . . . . . . . . . . . . . . . . . 9
1.3 The Brain as a Complex System. . . . . . . . . . . . . . . . . . . . . . . . .. 10
1.4 Traditional Versus Synergetic Interpretations
of Brain Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10
2. Exploring the Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
2.1 The Black Box Approach. .. .. . . . . . . . . . . . .. . . . . . . . . . . . . .. 13
2.2 Opening the Black Box. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14
2.3 Structure and Function at the Macroscopic Level. . . . . . . . . .. 14
2.4 Noninvasive Methods ................................... 16
2.4.1 X-Ray Tomography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
2.4.2 Electro-encephalograms (EEG) . . . . . . . . . . . . . . . . . . . .. 17
2.4.3 Magneto-encephalograms (MEG) . . . . . . . . . . . . . . . . . .. 18
2.4.4 Positron Emission Tomography (PET) . . . . . . . . . . . . .. 21
2.4.5 Magnetic Resonance Imaging (MRI) . . . . . . . . . . . . . . .. 23
2.5 Structure and Function at the Microscopic Level ........... 27
2.6 Learning and Memory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30
3. Modeling the Brain. A First Attempt:
The Brain as a Dynamical System ........................ 31
3.1 What Are Dynamical Systems? .......................... 31
3.2 The Brain as a Dynamical System. . . . . . . . . . . . . . . . . . . . . . .. 33
4. Basic Concepts of Synergetics I:
Order Parameters and the Slaving Principle . . . . . . . . . . . . .. 35
4.1 Factors Determining Temporal Evolution. . . . . . . . . . . . . . . . .. 35
4.2 Strategy of Solution .................................... 39
X Table of Contents
4.2.1 Instability, Order Parameters, Slaving Principle. . . . .. 39
4.2.2 The Laser Paradigm or Boats on a Lake. . . . . . . . . . . .. 44
4.2.3 The Slaving Principle. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45
4.2.4 The Central Role of Order Parameters. . . . . . . . . . . . .. 47
4.3 Self-Organization and the Second Law of Thermodynamics .. 48
5. Dynamics of Order Parameters. . . . . . . . . . . . . . . . . . . . . . . . . .. 51
5.1 One Order Parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51
5.2 Two Order Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
5.3 Three and More Order Parameters ....................... 61
5.4 Order Parameters and Normal Forms *. . . . . . . . . . . . . . . . . . .. 61
Part 11 Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65
6. Movement Coordination - Movement Patterns ........... 67
6.1 The Coordination Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68
6.2 Phase Transitions in Finger Movement:
Experiments and a Simple Model. . . . . . . . . . . . . . . . . . . . . . . .. 68
6.3 An Alternative Model? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74
* ...............
6.4 Fluctuations in Finger Movement: Theory 75
6.5 Critical Fluctuations in Finger Movements: Experiments .... 82
6.5.1 The Experimental Set-Up ......................... 82
6.5.2 Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84
6.6 Some Important Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 87
7. More on Finger Movements .............................. 91
7.1 Movement of a Single Index Finger. . . . . . . . . . . . . . . . . . . . . .. 91
7.2 Coupled Movement of Index Fingers. . . . . . . . . . . . . . . . . . . . .. 96
7.3 Phase Transitions in Human Hand Movements
During Multifrequency Tapping Tasks. . . . . . . . . . . . . . . . . . . .. 99
7.3.1 Experiment: Transitions in Multifrequency Tapping. .. 99
7.4 A Model for Multifrequency Behavior * ................... 103
* .........
7.5 The Basic Locking Equations and Their Solutions 106
7.6 Summary of the Main Theoretical Results ................. 113
7.7 Summary and Outlook .................................. 115
8. Learning .................................................. 117
8.1 How Learning Changes Order Parameter Landscapes ........ 117
8.2 How Learning Changes the Number of Order Parameters .... 121
8.3 How Learning Gives Rise to New Order Parameters ......... 122
*
Marks chapters or sections that are mathematically somewhat more involved
Table of Contents XI
9. Animal Gaits and Their Transitions .. .................... 123
9.1 Introductory Remarks ................................... 123
9.2 Symmetries and Groups ................................. 123
9.3 An Empirical Study of Quadruped Gaits .................. 128
9.4 Phase Dynamics and Symmetries ......................... 133
9.5 Equations of Phase Dynamics ............................ 138
9.6 Stationary Solutions .................................... 141
9.7 Gait Dynamics of Lower Symmetry ....................... 144
9.8 Summary and Outlook .................................. 146
10. Basic Concepts of Synergetics 11:
Formation of Spatia-temporal Patterns ................... 149
* ...................
11. Analysis of Spatio-temporal Patterns 157
11.1 Karhunen-Loeve Expansion, Singular Value Decomposition,
Principal Component Analysis -
Three Names for the Same Method ....................... 157
11.2 A Geometric Approach Based on Order Parameters.
The Haken-Friedrich-Uhl Method ........................ 164
11.2.1 One Real Order Parameter ........................ 164
11.2.2 Oscillations Connected
with One Complex Order Parameter ................ 171
12. Movements on a Pedalo .................................. 173
12.1 The Task .............................................. 173
12.2 Description of the Movement Pattern ..................... 174
12.3 Quantification of the Pedalo Movement .................... 175
12.4 Analysis of the Movement
Using the Karhunen-Loeve Expansion ..................... 176
12.5 A Detailed Analysis of the Movements of Arms and Legs .... 179
12.6 Haken-Friedrich-Uhl Order Parameter Analysis ............ 180
12.7 Concluding Remarks on Part II .......................... 191
Part III EEG and MEG ...................................... 193
13. Chaos, Chaos, Chaos ..................................... 195
14. Analysis of Electroencephalograms ....................... 203
14.1 Goals of the Analysis ................................... 203
14.2 Identification of Order Parameters and Spatial Modes ....... 204
14.3 Results ................................................ 209
15. Analysis of MEG Patterns ................................ 219
15.1 Experimental Results ................................... 219