Table of contents

  1. Front Matter
    Pages I-VIII
  2. Introduction

    1. Yoshiki Kuramoto
      Pages 1-4
  3. Methods

    1. Yoshiki Kuramoto
      Pages 5-21
    2. Yoshiki Kuramoto
      Pages 22-34
    3. Yoshiki Kuramoto
      Pages 35-59
  4. Applications

    1. Yoshiki Kuramoto
      Pages 60-88
    2. Yoshiki Kuramoto
      Pages 89-110
    3. Yoshiki Kuramoto
      Pages 111-140
  5. Back Matter
    Pages 141-158

About this book

Introduction

Tbis book is intended to provide a few asymptotic methods which can be applied to the dynamics of self-oscillating fields of the reaction-diffusion type and of some related systems. Such systems, forming cooperative fields of a large num­ of interacting similar subunits, are considered as typical synergetic systems. ber Because each local subunit itself represents an active dynamical system function­ ing only in far-from-equilibrium situations, the entire system is capable of showing a variety of curious pattern formations and turbulencelike behaviors quite unfamiliar in thermodynamic cooperative fields. I personally believe that the nonlinear dynamics, deterministic or statistical, of fields composed of similar active (Le., non-equilibrium) elements will form an extremely attractive branch of physics in the near future. For the study of non-equilibrium cooperative systems, some theoretical guid­ ing principle would be highly desirable. In this connection, this book pushes for­ ward a particular physical viewpoint based on the slaving principle. The dis­ covery of tbis principle in non-equilibrium phase transitions, especially in lasers, was due to Hermann Haken. The great utility of this concept will again be dem­ onstrated in tbis book for the fields of coupled nonlinear oscillators.

Keywords

Diffusion Oscillation behavior bifurcation dynamical system dynamical systems dynamics equilibrium fields nonlinear dynamics phase phase transition physics solution turbulence

Authors and affiliations

  • Yoshiki Kuramoto
    • 1
  1. 1.Research Institute for Fundamental PhysicsYukawa Hall, Kyoto UniversityKyoto 606Japan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-69689-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1984
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-69691-6
  • Online ISBN 978-3-642-69689-3
  • Series Print ISSN 0172-7389
  • About this book