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Lecture Notes on Mathematical Modelling in the Life Sciences

Waves in Neural Media

From Single Neurons to Neural Fields

Authors: Bressloff, Paul C.

  • ​Covers an extensive array of topics ranging from sub-cellular to tissue level biology
  • Can serve as an entry point for biologists wishing to learn about mathematical modeling
  • Provides an excellent introduction to mathematical neuroscience from the perspective of dymanical systems
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eBook $99.00
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  • ISBN 978-1-4614-8866-8
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  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-1-4614-8865-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this book

Waves in Neural Media: From Single Neurons to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weakly nonlinear analysis, Evans functions and wave stability, homogenization theory and averaging, and stochastic processes. Also covered in the text are exact methods of solution where applicable. Historically speaking, the propagation of action potentials has inspired new mathematics, particularly with regard to the PDE theory of waves in excitable media. More recently, continuum neural field models of large-scale brain networks have generated a new set of interesting mathematical questions with regard to the solution of nonlocal integro-differential equations. 

Advanced graduates, postdoctoral researchers and faculty working in mathematical biology, theoretical neuroscience, or applied nonlinear dynamics will find this book to be a valuable resource. The main prerequisites are an introductory graduate course on ordinary differential equations or partial differential equations, making this an accessible and unique contribution to the field of mathematical biology. 

Reviews

“This is a summary of the mathematical modeling of the dendrites, single and multi- neuronal units. … I think this book will appeal to neuromathematicians, researchers, graduate students, fellows, and theoretical neuroscientists.” (Joseph J. Grenier, Amazon.com, November, 2015)


Table of contents (9 chapters)

  • Single Neuron Modeling

    Bressloff, Paul C.

    Pages 3-62

  • Traveling Waves in One-Dimensional Excitable Media

    Bressloff, Paul C.

    Pages 63-99

  • Wave Propagation Along Spiny Dendrites

    Bressloff, Paul C.

    Pages 101-136

  • Calcium Waves and Sparks

    Bressloff, Paul C.

    Pages 137-181

  • Waves in Synaptically Coupled Spiking Networks

    Bressloff, Paul C.

    Pages 185-231

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4614-8866-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-1-4614-8865-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Waves in Neural Media
Book Subtitle
From Single Neurons to Neural Fields
Authors
Series Title
Lecture Notes on Mathematical Modelling in the Life Sciences
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-8866-8
DOI
10.1007/978-1-4614-8866-8
Softcover ISBN
978-1-4614-8865-1
Series ISSN
2193-4789
Edition Number
1
Number of Pages
XIX, 436
Number of Illustrations and Tables
133 b/w illustrations, 18 illustrations in colour
Topics