Haken H. Brain Dynamics. An Introduction to Models and Simulations

Berlin: Springer-Verlag. – 2008. – 355 p. (Springer Series in Synergetics) The great interest and favorable response this book has found among students, professors and other scientists working in a variety of disciplines related to brain dynamics has made a second edition necessary. Research on the human brain has become a truly interdisciplinary enterprise that no longer belongs to medicine, neurobiology and related fields alone. In fact, in our attempts to understand the functioning of the human brain, more and more concepts from physics, mathematics, computer science, mathematical biology and related fields are used. This list is by no means complete, but it reflects the aim of the present book. It will show how concepts and mathematical tools of these fields allow us to treat important aspects of the behavior of large networks of the building blocks of the brain, the neurons. This book applies to graduate students, professors and researchers in the above-mentioned fields, whereby I aimed throughout at a pedagogical style. A basic knowledge of calculus should be sufficient. In view of the various backgrounds of the readers of my book, I wrote several introductory chapters. For those who have little or no knowledge of the basic facts of neurons that will be needed later I included two chapters. Readers from the field of neuroscience, but also from other disciplines, will find the chapter on mathematical concepts and tricks useful. It shows how to describe spiking neurons and contains material that cannot easily be found in conventional textbooks, e.g. on the handling of δ-functions. Noise in physical systems – and thus also in the brain – is inevitable. This is true for systems in thermal equilibrium, but still more so in active systems – and neuronal systems are indeed highly active. Therefore, I deal with the origin and effects of noise in such systems. Contents
BASIC EXPERIMENTAL FACTS AND THEORETICAL TOOLSThe Neuron – Building Block of the Brain
Neuronal Cooperativity
Spikes, Phases, Noise: How to Describe Them Mathematically? We Learn a Few Tricks and Some Important Concepts
SPIKING IN NEURAL NETS
The Lighthouse Model. Two Coupled Neurons
The Lighthouse Model. Many Coupled Neurons
Integrate and Fire Models (IFM)
Many Neurons, General Case, ConnectionwithIntegrateandFireModel
Pattern Recognition Versus Synchronization: Pattern Recognition
Pattern Recognition Versus Synchronization: Synchronization and Phase Locking
PHASE LOCKING, COORDINATION AND SPATIO-TEMPORAL PATTERNS
Phase Locking via Sinusoidal Couplings
Pulse-Averaged EquationsThe Single Neuron
Conclusion and Outlook
Solutions to Exercises