Main Data
Author: Hermann Haken
Title: Brain Dynamics An Introduction to Models and Simulations
Publisher: Springer-Verlag
ISBN/ISSN: 9783540752387
Edition: 2
Price: CHF 86.20
Publication date: 01/01/2007
Category: Informatik, EDV Buch
Language: English
Technical Data
Pages: 333
Kopierschutz: DRM
Geräte: PC/MAC/eReader/Tablet
Formate: PDF
Table of contents

This is an excellent introduction for graduate students and nonspecialists to the field of mathematical and computational neurosciences. The book approaches the subject via pulsed-coupled neural networks, which have at their core the lighthouse and integrate-and-fire models. These allow for highly flexible modeling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. The more advanced pulse-averaged equations are discussed.

Table of contents
Foreword to the Second Edition6
Part I Basic Experimental Facts and Theoretical Tools14
1. Introduction15
1.1 Goal15
1.2 Brain: Structure and Functioning. A Brief Reminder16
1.3 Network Models17
1.4 How We Will Proceed19
2. The Neuron  Building Block of the Brain20
2.1 Structure and Basic Functions20
2.2 Information Transmission in an Axon21
2.3 Neural Code23
2.4 Synapses  The Local Contacts24
2.5 NakaRushton Relation25
2.6 Learning and Memory27
2.7 The Role of Dendrites27
3. Neuronal Cooperativity28
3.1 Structural Organization28
3.2 Global Functional Studies. Location of Activity Centers34
3.3 Interlude: A Minicourse on Correlations36
3.4 Mesoscopic Neuronal Cooperativity42
4. Spikes, Phases, Noise: How to Describe Them Mathematically? We Learn a Few Tricks and Some Important Concepts48
4.1 The d-Function and Its Properties48
4.2 Perturbed Step Functions54
4.3 Some More Technical Considerations*57
4.4 Kicks59
4.5 Many Kicks62
4.6 Random Kicks or a Look at Soccer Games63
4.7 Noise Is Inevitable. Brownian Motion and the Langevin Equation65
4.8 Noise in Active Systems67
4.9 The Concept of Phase71
4.10 Phase Noise79
4.11 Origin of Phase Noise*82
Part II Spiking in Neural Nets85
5. The Lighthouse Model. Two Coupled Neurons86
5.1 Formulation of the Model86
5.2 Basic Equations for the Phases of Two Coupled Neurons89
5.3 Two Neurons: Solution of the Phase-Locked State91
5.4 Frequency Pulling and Mutual Activation of Two Neurons95
5.5 Stability Equations98
5.6 Phase Relaxation and the Impact of Noise103
5.7 Delay Between Two Neurons107
5.8 An Alternative Interpretation of the Lighthouse Model109
6. The Lighthouse Model. Many Coupled Neurons111
6.1 The Basic Equations111
6.2 A Special Case. Equal Sensory Inputs. No Delay113
6.3 A Further Special Case. Different Sensory Inputs, but No Delay and No Fluctuations115
6.4 Associative Memory and Pattern Filter117
6.5 Weak Associative Memory. General Case*121
6.6 The Phase-Locked State of N Neurons. Two Delay Times124
6.7 Stability of the Phase-Locked State. Two Delay Times*126
6.8 Many Different Delay Times*131
6.9 Phase Waves in a Two-Dimensional Neural Sheet132
6.10 Stability Limits of Phase-Locked State133
6.11 Phase Noise*134
6.12 Strong Coupling Limit. The Nonsteady Phase- Locked State of Many Neurons138
6.13 Fully Nonlinear Treatment of the Phase- Locked State*142
7. Integrate and Fire Models (IFM)148
7.1 The General Equations of IFM148
7.2 Peskins Model150
7.3 A Model with Long Relaxation Times of Synaptic and Dendritic Responses152
8. Many Neurons, General Case, Connection with Integrate and Fire Model158
8.1 Introductory Remarks158
8.2 Basic Equations Including Delay and Noise158
8.3 Response of Dendritic Currents160
8.4 The Phase-Locked State162
8.5 Stability of the Phase-Locked State: Eigenvalue Equations163
8.6 Example of the Solution of an Eigenvalue Equation of the Form of ( 8.59)166
8.7 Stability of Phase-Locked State I: The Eigenvalues168
8.8 Stability of Phase-Locked State II: The Eigenvalues of the Integrate and Fire Model169
8.9 Generalization to Several Delay Times172
8.10 Time-Dependent Sensory Inputs173
8.11 Impact of Noise and Delay174
8.12 Partial Phase Locking174
8.13 Derivation of Pulse-Averaged Equations175
Appendix 1 to Chap. 8: Evaluation of (8.35)179
Appendix 2 to Chap. 8: Fractal Derivatives183
9. Pattern Recognition Versus Synchronization: Pattern Recognition186
9.1 Introduction186
9.2 Basic Equations187
9.3 A Reminder of Pattern Recognition by the Synergetic Computer and an Alternative Approach190
9.4 Properties of the Synergetic Computer of Type II193
9.5 Limit of Dense Pulses198
9.6 Pulse Rates Are Positive203
9.7 Chopped Signals. Quasi-Attractors205
9.8 Appendix to Sect. 9.5208
10. Pattern Recognition Versus Synchronization: Synchronization and Phase Locking211
10.1 The Synchronized State211
10.2 Stability of the Synchronized State216
10.3 Stability Analysis Continued: Solution of the Stability Equations219
10.4 Generalization to More Complicated Dendritic Responses*223
10.5 Stability Analysis for the General Case of Dendritic Responses*227
10.6 From Synchronization to Phase Locking231
10.7 Conclusion to Chaps. 9 and 10: Two Pathways to Pattern Recognition238
Part III Phase Locking, Coordination and Spatio- Temporal Patterns240
11. Phase Locking via Sinusoidal Couplings241
11.1 Coupling Between Two Neurons241
11.2 A Chain of Coupled-Phase Oscillators244
11.3 Coupled Finger Movements246
11.4 Quadruped Motion249
11.5 Populations of Neural Phase Oscillators251
12. Pulse-Averaged Equations253
12.1 Survey253
12.2 The WilsonCowan Equations254
12.3 A Simple Example255
12.4 Cortical Dynamics Described by WilsonCowan Equations260
12.5 Visual Hallucinations262
12.6 JirsaHakenNunez Equations263