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Foundations of Synergetics I

Distributed Active Systems

  • Book
  • © 1990

Overview

Authors:
  1. Alexander S. Mikhailov

    1. Department of Physics, Moscow State University, Moscow, USSR

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Part of the book series: Springer Series in Synergetics (SSSYN, volume 51)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Alexander S. Mikhailov
    Pages 1-13

  3. Bistable Media

    • Alexander S. Mikhailov
    Pages 14-31

  4. Excitable Media

    • Alexander S. Mikhailov
    Pages 32-80

  5. Oscillatory Media

    • Alexander S. Mikhailov
    Pages 81-98

  6. Active Media with Long-Range Inhibition

    • Alexander S. Mikhailov
    Pages 99-112

  7. Neural Networks

    • Alexander S. Mikhailov
    Pages 113-154

  8. Reproductive Networks

    • Alexander S. Mikhailov
    Pages 155-176

  9. Back Matter

    Pages 177-189
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Keywords

About this book

This book gives an introduction to the mathematical theory of cooperative behavior in active systems of various origins, both natural and artificial. It is based on a lecture course in synergetics which I held for almost ten years at the University of Moscow. The first volume deals mainly with the problems of pattern fonnation and the properties of self-organized regular patterns in distributed active systems. It also contains a discussion of distributed analog information processing which is based on the cooperative dynamics of active systems. The second volume is devoted to the stochastic aspects of self-organization and the properties of self-established chaos. I have tried to avoid delving into particular applications. The primary intention is to present general mathematical models that describe the principal kinds of coopera­ tive behavior in distributed active systems. Simple examples, ranging from chemical physics to economics, serve only as illustrations of the typical context in which a particular model can apply. The manner of exposition is more in the tradition of theoretical physics than of in mathematics: Elaborate fonnal proofs and rigorous estimates are often replaced the text by arguments based on an intuitive understanding of the relevant models. Because of the interdisciplinary nature of this book, its readers might well come from very diverse fields of endeavor. It was therefore desirable to minimize the re­ quired preliminary knowledge. Generally, a standard university course in differential calculus and linear algebra is sufficient.

Authors and Affiliations

  • Department of Physics, Moscow State University, Moscow, USSR

    Alexander S. Mikhailov

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