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