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

339 Pages·1996·11.58 MB·English
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Principles of Brain Functioning Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milano Paris Santa Clara Singapur Tokyo 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 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable 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 regulations and therefore free for general use. 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

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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
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