**CRM Monograph Series**

Volume: 7;
1996;
125 pp;
Hardcover

MSC: Primary 92;
Secondary 39

Print ISBN: 978-0-8218-0458-2

Product Code: CRMM/7

List Price: $46.00

Individual Member Price: $36.80

**Electronic ISBN: 978-1-4704-3853-1
Product Code: CRMM/7.E**

List Price: $46.00

Individual Member Price: $36.80

# Dynamics of Small Neural Populations

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*John Milton*

A co-publication of the AMS and Centre de Recherches Mathématiques

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.

Features:

- 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.

#### Readership

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

#### Reviews & Endorsements

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

# Table of Contents

## Dynamics of Small Neural Populations

- Cover Cover11
- Title page iii4
- Dedication v6
- Quote vii8
- Contents ix10
- List of Figures xi12
- List of Tables xv16
- Preface xvii18
- Chapter 1. Introduction 120
- Chapter 2. Input-output relationships 1130
- Chapter 3. Chance or chaos? 2140
- Chapter 4. Recurrent inhibition 3352
- Chapter 5. Negative feedback control 4766
- Chapter 6. Complex Neural Dynamics 6988
- Chapter 7. Noise and neural dynamics 81100
- Chapter 8. Neural populations 95114
- Chapter 9. Concluding remarks 111130
- Appendix A. Poisson processes 113132
- Bibliography 115134
- Back Cover Back Cover1145