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Dynamics of Small Neural Populations
John Milton, University of Chicago, IL
A co-publication of the AMS and Centre de Recherches Mathématiques.

CRM Monograph Series
1996; 125 pp; hardcover
Volume: 7
ISBN-10: 0-8218-0458-8
ISBN-13: 978-0-8218-0458-2
List Price: US$46
Member Price: US$36.80
Order Code: CRMM/7
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This book arose from a series of lectures presented at the CRM Summer School in Mathematical Biology held at the University of British Columbia in the summer of 1993 by John Milton, a clinical neurologist and biomathematician. In this work, three themes are explored: time-delayed feedback control, noise, and statistical properties of neurons and large neural populations.

This volume focuses on systems composed of 2-3 neurons. Such neural populations are small enough to permit experimental manipulation while at the same time are well enough characterized so that plausible mathematical models can be posed. Thus, direct comparisons between theory and observation are in principle possible.


  • First text to review the effects of time delays and noise on neural control.
  • Accessible to both neurobiologists and mathematicians.
  • Emphasis on problems for which comparisons between observation and prediction are possible.
  • Self-contained and succinctly written.
  • Excellent source for potential research topics.

Titles in this series are co-published with the Centre de Recherches Mathématiques.


Advanced undergraduate students, graduate students, research mathematicians, control systems engineers, and neurobiologists interested in mathematical neurobiology.


"Style is quite accessible ... good for supplementary reading for both mathematical biology and neuroscience courses ... carefully edited and the references ... give the reader an indication of the scope of work done on these and related problems ... gives starting points for further investigations in many directions."

-- Bulletin of Mathematical Biology

"It is easy to get a good introduction to time-delayed neural feedback mechanisms from this book because all concepts, mathematical as well as neurophysiological, are well explained, and the bibliography is exhaustive and referred to right through the text."

-- Mathematical Reviews

Table of Contents

  • Introduction
  • Input-output relationships
  • Chance or chaos?
  • Recurrent inhibition
  • Negative feedback control
  • Complex neural dynamics
  • Noise and neural dynamics
  • Neural populations
  • Concluding remarks
  • Appendix A. Poisson processes
  • Bibliography
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