Chemical Oscillations, Waves, and Turbulence

1. Front Matter

   Pages I-VIII

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2. Introduction

   1. Introduction

      • Yoshiki Kuramoto

      Pages 1-4

3. Methods

   1. Reductive Perturbation Method

      • Yoshiki Kuramoto

      Pages 5-21

   2. Method of Phase Description I

      • Yoshiki Kuramoto

      Pages 22-34

   3. Method of Phase Description II

      • Yoshiki Kuramoto

      Pages 35-59

4. Applications

   1. Mutual Entrainment

      • Yoshiki Kuramoto

      Pages 60-88

   2. Chemical Waves

      • Yoshiki Kuramoto

      Pages 89-110

   3. Chemical Turbulence

      • Yoshiki Kuramoto

      Pages 111-140

5. Back Matter

   Pages 141-158

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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.

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

• Research Institute for Fundamental Physics, Yukawa Hall, Kyoto University, Kyoto 606, Japan

  Yoshiki Kuramoto

Policies and ethics