Weakly Connected Neural Networks

  • Frank C. Hoppensteadt
  • Eugene M. Izhikevich

Part of the Applied Mathematical Sciences book series (AMS, volume 126)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 3-24
    3. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 25-101
    4. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 103-110
    5. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 111-139
  3. Derivation of Canonical Models

    1. Front Matter
      Pages 141-141
    2. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 143-187
    3. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 189-207
    4. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 209-218
    5. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 219-245
    6. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 247-293
  4. Analysis of Canonical Models

    1. Front Matter
      Pages 295-295
    2. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 297-309
    3. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 311-335
    4. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 337-351
    5. Frank C. Hoppensteadt, Eugene M. Izhikevich
      Pages 353-379
  5. Back Matter
    Pages 381-402

About this book

Introduction

This book is devoted to an analysis of general weakly connected neural networks (WCNNs) that can be written in the form (0.1) m Here, each Xi E IR is a vector that summarizes all physiological attributes of the ith neuron, n is the number of neurons, Ii describes the dynam­ ics of the ith neuron, and gi describes the interactions between neurons. The small parameter € indicates the strength of connections between the neurons. Weakly connected systems have attracted much attention since the sec­ ond half of seventeenth century, when Christian Huygens noticed that a pair of pendulum clocks synchronize when they are attached to a light­ weight beam instead of a wall. The pair of clocks is among the first weakly connected systems to have been studied. Systems of the form (0.1) arise in formal perturbation theories developed by Poincare, Liapunov and Malkin, and in averaging theories developed by Bogoliubov and Mitropolsky.

Keywords

biology calculus differential equation neural network neurons neuroscience

Authors and affiliations

  • Frank C. Hoppensteadt
    • 1
  • Eugene M. Izhikevich
    • 1
  1. 1.Center for Systems Science and EngineeringArizona State UniversityTempeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1828-9
  • Copyright Information Springer Science+Business Media New York 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7302-8
  • Online ISBN 978-1-4612-1828-9
  • Series Print ISSN 0066-5452
  • About this book