Neural Fields

Theory and Applications

Editors: Coombes, S., beim Graben, P., Potthast, R., Wright, J. (Eds.)

  • Written by leading scientists in the field
  • Includes contributions from two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan
  • The first comprehensive collection of results in the research area of neural field theory
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eBook $109.00
price for USA (gross)
  • ISBN 978-3-642-54593-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-642-54592-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-662-51511-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.

Table of contents (18 chapters)

  • Tutorial on Neural Field Theory

    Coombes, Stephen (et al.)

    Pages 1-43

  • A Personal Account of the Development of the Field Theory of Large-Scale Brain Activity from 1945 Onward

    Cowan, Jack

    Pages 47-96

  • Heaviside World: Excitation and Self-Organization of Neural Fields

    Amari, Shun-ichi

    Pages 97-118

  • Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation

    Ermentrout, G. Bard (et al.)

    Pages 119-151

  • PDE Methods for Two-Dimensional Neural Fields

    Laing, Carlo R.

    Pages 153-173

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-642-54593-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-642-54592-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-662-51511-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Neural Fields
Book Subtitle
Theory and Applications
Editors
  • Stephen Coombes
  • Peter beim Graben
  • Roland Potthast
  • James Wright
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-54593-1
DOI
10.1007/978-3-642-54593-1
Hardcover ISBN
978-3-642-54592-4
Softcover ISBN
978-3-662-51511-2
Edition Number
1
Number of Pages
X, 487
Number of Illustrations and Tables
82 b/w illustrations, 50 illustrations in colour
Topics