Description: Chemical Oscillations, Waves, and Turbulence by Y. Kuramoto A fundamental and frequently cited book provides asymptotic methods applicable to the dynamics of self-oscillating fields of the reaction-diffusion type. Graduate level. 40 figures. 1984 edition. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description This highly respected, frequently cited book addresses two exciting fields: pattern formation and synchronization of oscillators. It systematically develops the dynamics of many-oscillator systems of dissipative type, with special emphasis on oscillating reaction-diffusion systems. The author applies the reductive perturbation method and the phase description method to the onset of collective rhythms, the formation of wave patterns, and diffusion-induced chemical turbulence.This two-part treatment starts with a section on methods, defining and exploring the reductive perturbation method - oscillators versus fields of oscillators, the Stuart-Landau equation, onset of oscillations in distributed systems, and the Ginzburg-Landau equations. It further examines methods of phase description, including systems of weakly coupled oscillators, one-oscillator problems, nonlinear phase diffusion equations, and representation by the Floquet eigenvectors.Additional methods include systematic perturbation expansion, generalization of the nonlinear phase diffusion equation, and the dynamics of both slowly varying wavefronts and slowly phase-modulated periodic waves. The second part illustrates applications, from mutual entrainment to chemical waves and chemical turbulence. The text concludes with a pair of convenient appendixes. Table of Contents 1. Introduction Part 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 Part 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 Appendix A. Plane Wave Solutions of the Ginzburg-Landau Equation B. The Hopf Bifurication for the Brusselator References Subject Index Long Description A fundamental and frequently cited book in two very exciting fields: pattern formation and synchronization of oscillators. Provides asymptotic methods that can be applied to the dynamics of self-oscillating fields of the reaction-diffusion type and of some related systems. Graduate level. 40 figures. Details ISBN0486428818 Short Title CHEMICAL OSCILLATIONS WAVES & Language English ISBN-10 0486428818 ISBN-13 9780486428819 Media Book Format Paperback DEWEY 003 Year 2003 Imprint Dover Publications Inc. Place of Publication New York Country of Publication United States Series Dover Books on Chemistry Illustrations black & white illustrations DOI 10.1604/9780486428819 UK Release Date 2003-05-26 AU Release Date 2003-05-26 NZ Release Date 2003-05-26 US Release Date 2003-05-26 Author Y. Kuramoto Pages 164 Publisher Dover Publications Inc. Publication Date 2003-05-26 Audience General We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:78525446;
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ISBN-13: 9780486428819
Book Title: Chemical Oscillations, Waves, and Turbulence
Publisher: Dover Publications Inc.
Publication Year: 2003
Subject: Chemistry
Item Height: 234 mm
Number of Pages: 164 Pages
Language: English
Publication Name: Chemical Oscillations, Waves, and Turbulence
Type: Textbook
Author: Y. Kuramoto
Item Width: 154 mm
Format: Paperback