Brain Dynamics

1. Front Matter

   Pages I-XII

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2. Basic Experimental Facts and Theoretical Tools

   1. Front Matter

      Pages 1-1

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   2. Introduction

      Pages 3-7

   3. The Neuron — Building Block of the Brain

      Pages 9-16

   4. Neuronal Cooperativity

      Pages 17-36

   5. Spikes, Phases, Noise: How to Describe Them Mathematically? We Learn a Few Tricks and Some Important Concepts

      Pages 37-73

3. Spiking in Neural Nets

   1. Front Matter

      Pages 75-75

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   2. The Lighthouse Model. Two Coupled Neurons

      Pages 77-101

   3. The Lighthouse Model. Many Coupled Neurons

      Pages 103-139

   4. Integrate and Fire Models (IFM)

      Pages 141-150

   5. Many Neurons, General Case, Connection with Integrate and Fire Model

      Pages 151-179

4. Phase Locking, Coordination and Spatio-Temporal Patterns

   1. Front Matter

      Pages 181-181

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   2. Phase Locking via Sinusoidal Couplings

      Pages 183-194

   3. Pulse-Averaged Equations

      Pages 195-213

5. Conclusion

   1. Front Matter

      Pages 215-215

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   2. The Single Neuron

      Pages 217-224

   3. Conclusion and Outlook

      Pages 225-227

6. Back Matter

   Pages 229-248

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Twenty-Five Years of Springer Series in Synergetics The year 2002 marks the 25th anniversary of the Springer Series in S- ergetics. It started in 1977 with my book “Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Ch- istry and Biology”. In the near future, the 100th volume of this series will be published. Its success has been made possible by the contributions of outstanding authors who presented their quite often pioneering results to the science community well beyond the borders of a special discipline. Indeed, interdisciplinarity is one of the main features of this series. But interdis- plinarity is not enough: The main goal is the search for common features of self-organizing systems in a great variety of seemingly quite di?erent systems, or, still more precisely speaking, the search for general principles underlying the spontaneous formation of spatial, temporal or functional structures. The objects studied may be as diverse as lasers and ?uids in physics, pattern formation in chemistry, morphogenesis in biology, brain functions in neur- ogy or self-organization in a city. As is witnessed by several volumes, great attention is being paid to the pivotal interplay between deterministic and stochastic processes, as well as to the dialogue between theoreticians and experimentalists. All this has contributed to a remarkable cross-fertilization between disciplines and to a deeper unterstanding of complex systems. The timeliness and potential of such an approach are also mirrored – among other indicators – bynumerous interdisciplinary workshops and conferencesall over the world.

• Computational Neuroscience
• Dynamical Systems
• Movement control
• Neural Nets
• Neuronal Systems
• Synapse
• Synaptic Models
• artificial intelligence
• neurons

From the reviews:

“This book focuses on synchronization of coupled systems of neuronal phase models the author calls ‘lighthouse models.’ … the book is an interesting read, and it will be of interest to computational neuroscientists working in synchrony and maybe mean-field models.” (Andrea K. Barreiro, SIAM Review, Vol. 52 (2), 2010)

• Institut für theoretische Physik und Synergetik, Universität Stuttgart, Stuttgart, Germany

  Hermann Haken

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