Chemical oscillations, waves, and turbulence

Author(s)

• 蔵本, 由紀 クラモト, ヨシキ

Bibliographic Information

Chemical oscillations, waves, and turbulence

Y. Kuramoto

（Springer series in synergetics, v. 19）

Springer-Verlag, 1984

• : U.S.
• : Germany
• : pbk

Note

Bibliography: p. [149]-153

Includes index

Description and Table of Contents

Volume

: Germany ISBN 9783540133223

Description

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.

Table of Contents

1.- I Methods.- 2. Reductive Perturbation Method.- 2.1 Oscillators Versus Fields of Oscillators.- 2.2 The Stuart-Landau Equation.- 2.3 Onset of Oscillations in Distributed Systems.- 2.4 The Ginzburg-Landau Equation.- 3. Method of Phase Description I.- 3.1 Systems of Weakly Coupled Oscillators.- 3.2 One-Oscillator Problem.- 3.3 Nonlinear Phase Diffusion Equation.- 3.4 Representation by the Floquet Eigenvectors.- 3.5 Case of the Ginzburg-Landau Equation.- 4. Method of Phase Description II.- 4.1 Systematic Perturbation Expansion.- 4.2 Generalization of the Nonlinear Phase Diffusion Equation.- 4.3 Dynamics of Slowly Varying Wavefronts.- 4.4 Dynamics of Slowly Phase-Modulated Periodic Waves.- II Applications.- 5. Mutual Entrainment.- 5.1 Synchronization as a Mode of Self-Organization.- 5.2 Phase Description of Entrainment.- 5.2.1 One Oscillator Subject to Periodic Force.- 5.2.2 A Pair of Oscillators with Different Frequencies.- 5.2.3 Many Oscillators with Frequency Distribution.- 5.3 Calculation of ? for a Simple Model.- 5.4 Soluble Many-Oscillator Model Showing Synchronization-Desynchronization Transitions.- 5.5 Oscillators Subject to Fluctuating Forces.- 5.5.1 One Oscillator Subject to Stochastic Forces.- 5.5.2 A Pair of Oscillators Subject to Stochastic Forces.- 5.5.3 Many Oscillators Which are Statistically Identical.- 5.6 Statistical Model Showing Synchronization-Desynchronization Transitions.- 5.7 Bifurcation of Collective Oscillations.- 6. Chemical Waves.- 6.1 Synchronization in Distributed Systems.- 6.2 Some Properties of the Nonlinear Phase Diffusion Equation.- 6.3 Development of a Single Target Pattern.- 6.4 Development of Multiple Target Patterns.- 6.5 Phase Singularity and Breakdown of the Phase Description.- 6.6 Rotating Wave Solution of the Ginzburg-Landau Equation.- 7. Chemical Turbulence.- 7.1 Universal Diffusion-Induced Turbulence.- 7.2 Phase Turbulence Equation.- 7.3 Wavefront Instability.- 7.4 Phase Turbulence.- 7.5 Amplitude Turbulence.- 7.6 Turbulence Caused by Phase Singularities.- A. Plane Wave Solutions of the Ginzburg-Landau Equation.- B. The Hopf Bifurcation for the Brusselator.- References.

Volume

: pbk ISBN 9783642696916

Description

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.

Table of Contents

1.- I Methods.- 2. Reductive Perturbation Method.- 2.1 Oscillators Versus Fields of Oscillators.- 2.2 The Stuart-Landau Equation.- 2.3 Onset of Oscillations in Distributed Systems.- 2.4 The Ginzburg-Landau Equation.- 3. Method of Phase Description I.- 3.1 Systems of Weakly Coupled Oscillators.- 3.2 One-Oscillator Problem.- 3.3 Nonlinear Phase Diffusion Equation.- 3.4 Representation by the Floquet Eigenvectors.- 3.5 Case of the Ginzburg-Landau Equation.- 4. Method of Phase Description II.- 4.1 Systematic Perturbation Expansion.- 4.2 Generalization of the Nonlinear Phase Diffusion Equation.- 4.3 Dynamics of Slowly Varying Wavefronts.- 4.4 Dynamics of Slowly Phase-Modulated Periodic Waves.- II Applications.- 5. Mutual Entrainment.- 5.1 Synchronization as a Mode of Self-Organization.- 5.2 Phase Description of Entrainment.- 5.2.1 One Oscillator Subject to Periodic Force.- 5.2.2 A Pair of Oscillators with Different Frequencies.- 5.2.3 Many Oscillators with Frequency Distribution.- 5.3 Calculation of ? for a Simple Model.- 5.4 Soluble Many-Oscillator Model Showing Synchronization-Desynchronization Transitions.- 5.5 Oscillators Subject to Fluctuating Forces.- 5.5.1 One Oscillator Subject to Stochastic Forces.- 5.5.2 A Pair of Oscillators Subject to Stochastic Forces.- 5.5.3 Many Oscillators Which are Statistically Identical.- 5.6 Statistical Model Showing Synchronization-Desynchronization Transitions.- 5.7 Bifurcation of Collective Oscillations.- 6. Chemical Waves.- 6.1 Synchronization in Distributed Systems.- 6.2 Some Properties of the Nonlinear Phase Diffusion Equation.- 6.3 Development of a Single Target Pattern.- 6.4 Development of Multiple Target Patterns.- 6.5 Phase Singularity and Breakdown of the Phase Description.- 6.6 Rotating Wave Solution of the Ginzburg-Landau Equation.- 7. Chemical Turbulence.- 7.1 Universal Diffusion-Induced Turbulence.- 7.2 Phase Turbulence Equation.- 7.3 Wavefront Instability.- 7.4 Phase Turbulence.- 7.5 Amplitude Turbulence.- 7.6 Turbulence Caused by Phase Singularities.- A. Plane Wave Solutions of the Ginzburg-Landau Equation.- B. The Hopf Bifurcation for the Brusselator.- References.

by "Nielsen BookData"

• NCID: BA00415145
• ISBN:
  • 0387133224
  • 3540133224
  • 9783642696916
• LCCN: 84005563
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: viii, 156 p.
• Size: 25 cm
• Classification:
  • DC19 : 003
  • NDLC : PA41
• Subject Headings:
  • LCSH : System theory
  • LCSH : Dynamics
  • LCSH : Self-organizing systems
  • LCSH : Chemistry, Physical and theoretical
• Parent Bibliography ID:
  • BA00004912