Chemical Oscillations, Waves and Turbulence
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Kuramoto (Kyoto U.) describes a few asymptotic methods that can be used to analyze the dynamics of self-oscillating fields of the reactive-diffusion type and some related systems, and surveys some applications of them. The original, published by Springer-Verlag in 1984, is here slightly corrected. Annotation ©2003 Book News, Inc., Portland, OR
1.Introduction1Part IMethods2.Reductive Perturbation Method52.1Oscillators Versus Fields of Oscillators52.2The Stuart-Landau Equation82.3Onset of Oscillations in Distributed Systems132.4The Ginzburg-Landau Equation173.Method of Phase Description223.1Systems of Weakly Coupled Oscillators223.2One-Oscillator Problem243.3Nonlinear Phase Diffusion Equation283.4Representation by the Floquet Eigenvectors293.5Case of the Ginzburg-Landau Equation324.Method of Phase Description II354.1Systematic Perturbation Expansion354.2Generalization of the Nonlinear Phase Diffusion Equation414.3Dynamics of Slowly Varying Wavefronts464.4Dynamics of Slowly Phase-Modulated Periodic Waves54Part IIApplications5.Mutual Entrainment605.1Synchronization as a Mode of Self-Organization605.2Phase Description of Entrainment625.2.1One Oscillator Subject to Periodic Force625.2.2A Pair of Oscillators with Different Frequencies655.2.3Many Oscillators with Frequency Distribution665.3Calculation of [Gamma] for a Simple Model675.4Soluble Many-Oscillator Model Showing Synchronization-Desynchronization Transitions685.5Oscillators Subject to Fluctuating Forces785.5.1One Oscillator Subject to Stochastic Forces785.5.2A Pair of Oscillators Subject to Stochastic Forces805.5.3Many Oscillators Which are Statistically Identical825.6Statistical Model Showing Synchronization-Desynchronization Transitions825.7Bifurcation of Collective Oscillations846.Chemical Waves896.1Synchronization in Distributed Systems896.2Some Properties of the Nonlinear Phase Diffusion Equation916.3Development of a Single Target Pattern936.4Development of Multiple Target Patterns1016.5Phase Singularity and Breakdown of the Phase Description1036.6Rotating Wave Solution of the Ginzburg-Landau Equation1067.Chemical Turbulence1117.1Universal Diffusion-Induced Turbulence1117.2Phase Turbulence Equation1147.3Wavefront Instability1207.4Phase Turbulence1277.5Amplitude Turbulence1327.6Turbulence Caused by Phase Singularities137Appendix141A.Plane Wave Solutions of the Ginzburg-Landau Equation141B.The Hopf Bifurcation for the Brusselator144References149Subject Index155
