Brain Dynamics
Synchronization and Activity Patterns in Pulse-Coupled Neural Nets with Delays and Noise
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Beschreibung
This book addresses a large variety of models in mathematical and computational neuroscience. It is written for the experts as well as for graduate students wishing to enter this fascinating field of research. The author studies the behaviour of large neural networks composed of many neurons coupled by spike trains. He devotes the main part to the synchronization problem. He presents neural net models more realistic than the conventional ones by taking into account the detailed dynamics of axons, synapses and dendrites, allowing rather arbitrary couplings between neurons. He gives a complete stabile analysis that goes significantly beyond what has been known so far. He also derives pulse-averaged equations including those of the Wilson--Cowan and the Jirsa-Haken-Nunez types and discusses the formation of spatio-temporal neuronal activity pattems. An analysis of phase locking via sinusoidal couplings leading to various kinds of movement coordination is included.
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.
Includes supplementary material: sn.pub/extras
Autor*in
Hermann Haken
Themen in »Brain Dynamics«
Computational Neuroscience Dynamical Systems Movement control Neural Nets Neuronal Systems Synapse Synaptic Models artificial intelligence neurons
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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)()