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.

Inhalt

Prologue.- I Foundations.- 1. Introduction.- 1.1 Biological Systems are Complex Systems.- 1.2 Goals of Synergetics.- 1.3 The Brain as a Complex System.- 1.4 Traditional Versus Synergetic Interpretations of Brain Functions.- 2. Exploring the Brain.- 2.1 The Black Box Approach.- 2.2 Opening the Black Box.- 2.3 Structure and Function at the Macroscopic Level.- 2.4 Noninvasive Methods.- 2.4.1 X-ray Tomography.- 2.4.2 Electro-encephalograms (EEG).- 2.4.3 Magneto-encephalograms (MEG).- 2.4.4 Positron Emission Tomography (PET).- 2.4.5 Magnetic Resonance Imaging (MRI).- 2.5 Structure and Function at the Microscopic Level.- 2.6 Learning and Memory.- 3. Modeling the Brain. A First Attempt: The Brain as a Dynamical System.- 3.1 What are Dynamical Systems?.- 3.2 The Brain as a Dynamical System.- 4. Basic Concepts of Synergetics I: Order Parameters and the Slaving Principle.- 4.1 Factors Determining Temporal Evolution.- 4.2 Strategy of Solution.- 4.2.1 Instability, Order Parameters, Slaving Principle.- 4.2.2 The Laser Paradigm or Boats on a Lake.- 4.2.3 The Slaving Principle.- 4.2.4 The Central Role of Order Parameters.- 4.3 Self-Organization and the Second Law of Thermodynamics.- 5. Dynamics of Order Parameters.- 5.1 One Order Parameter.- 5.2 Two Order Parameters.- 5.3 Three and More Order Parameters.- 5.4 Order Parameters and Normal Forms *.- II Behavior.- 6. Movement Coordination - Movement Patterns.- 6.1 The Coordination Problem.- 6.2 Phase Transitions in Finger Movement: Experiments and a Simple Model.- 6.3 An Alternative Model?.- 6.4 Fluctuations in Finger Movement: Theory *.- 6.5 Critical Fluctuations in Finger Movements: Experiments.- 6.5.1 The Experimental Set-Up.- 6.5.2 Experimental Results.- 6.6 Some Important Conclusions.- 7. More on Finger Movements.- 7.1 Movement of a Single Index Finger.- 7.2 Coupled Movement of Index Fingers.- 7.3 Phase Transitions in Human Hand Movements During Multifrequency Tapping Tasks.- 7.3.1 Experiment: Transitions in Multifrequency Tapping.- 7.4 A Model for Multifrequency Behavior *.- 7.5 The Basic Locking Equations and Their Solutions *.- 7.6 Summary of the Main Theoretical Results.- 7.7 Summary and Outlook.- 8. Learning.- 8.1 How Learning Changes Order Parameter Landscapes.- 8.2 How Learning Changes the Number of Order Parameters.- 8.3 How Learning Gives Rise to New Order Parameters.- 9. Animal Gaits and Their Transitions.- 9.1 Introductory Remarks.- 9.2 Symmetries and Groups.- 9.3 An Empirical Study of Quadruped Gaits.- 9.4 Phase Dynamics and Symmetries.- 9.5 Equations of Phase Dynamics.- 9.6 Stationary Solutions.- 9.7 Gait Dynamics of Lower Symmetry.- 9.8 Summary and Outlook.- 10. Basic Concepts of Synergetics II: Formation of Spatio-temporal Patterns.- 11. Analysis of Spatio-temporal Patterns *.- 11.1 Karhunen-Loève Expansion, Singular Value Decomposition, Principal Component Analysis - Three Names for the Same Method.- 11.2 A Geometric Approach Based on Order Parameters. The Haken-Friedrich-Uhl Method.- 11.2.1 One Real Order Parameter.- 11.2.2 Oscillations Connected with One Complex Order Parameter.- 12. Movements on a Pedalo.- 12.1 The Task.- 12.2 Description of the Movement Pattern.- 12.3 Quantification of the Pedalo Movement.- 12.4 Analysis of the Movement Using the Karhunen-Loève Expansion.- 12.5 A Detailed Analysis of the Movements of Arms and Legs.- 12.6 Haken-Priedrich-Uhl Order Parameter Analysis.- 12.7 Concluding Remarks on Part II.- III EEG and MEG.- 13. Chaos, Chaos, Chaos.- 14. Analysis of Electroencephalograms.- 14.1 Goals of the Analysis.- 14.2 Identification of Order Parameters and Spatial Modes.- 14.3 Results.- 15. Analysis of MEG Patterns.- 15.1 Experimental Results.- 15.2 Temporal and Spatial Analysis.- 15.2.1 Temporal Analysis.- 15.2.2 Spatio-temporal Analysis.- 15.3 Modeling the Dynamics.- 15.4 Modeling the Dynamics: Towards a Field Theory of Brain Activity.- 15.5 EEG and MEG Analysis Revisited.- IV Cognition.- 16. Visual Perception.- 16.1 A Model of Pattern Recognition.- 16.2 The Role of Attention Parameters. Ambiguous Figures.- 16.3 Influence of a Bias.- 16.4 The Role of Fluctuations of Attention Parameters.- 16.5 Learning Patterns.- 16.6 A Model for Stereo Vision.- 17. Decision Making as Pattern Recognition.- 18. The Brain as a Computer or Can Computers Think?.- 18.1 An Excursion: What is Thinking?.- 18.2 Computers.- 18.3 Artificial Intelligence.- 18.4 Neurocomputers and Connectionism.- 18.5 Can Computers Think?.- 19. Networks of Brains.- 19.1 A General Model of IRN in Terms of Synergetics.- 19.2 Collective Cognitive Processes.- 19.3 Iterations.- 19.4 Concluding Remarks.- 20. Synergetics of the Brain: Where Do We Stand? Where Do We Go from Here?.- 20.1 Looking Back.- 20.2 Mind and Matter - An Eternal Question.- 20.3 Some Open Problems.- Appendices.- A. Analysis of Time Series.- A.1 Time Series Analysis.- A.2 Definition of Dimensions.- A.3 Dimension of Attractors.- A.4 Some Conclusions.- B. Determination of Adjoint Vectors.- C. The Potentials Occurring in Sect. 16.5.- References and Further Reading.- About the Author.