Nonlinearities in Action: Oscillations Chaos Order Fractals

Nonlinearities in Action: Oscillations Chaos Order Fractals

Paperback(Softcover reprint of the original 1st ed. 1992)

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Product Details

ISBN-13: 9783642752940
Publisher: Springer Berlin Heidelberg
Publication date: 11/23/2011
Edition description: Softcover reprint of the original 1st ed. 1992
Pages: 191
Product dimensions: 7.60(w) x 10.63(h) x (d)

Table of Contents

1. Introduction.- 2. Nonlinear Oscillations and Waves. Classical Results.- 2.1 Oscillators.- 2.1.1 A Marble in the Chute.- 2.1.2 Spring Pendulum and Nonlinear Optics.- 2.1.3 Nonlinear Landau Damping and Amplification.- 2.2 Solitons.- 2.2.1 The Fermi-Pasta-Ulam Paradox.- 2.2.2 Solitons as Particles.- 2.2.3 Solitons and Shock Waves.- 2.3 Self-Excited Oscillations.- 2.3.1 Examples and Definitions.- 2.3.2 Competition and Synchronization.- 2.3.3 Self-Excited Oscillations in Chains and Continuous Systems.- 2.4 Bifurcations.- 2.4.1 Acquisition of a New Quality.- 2.4.2 Bifurcations of Equilibrium States.- 2.4.3 Bifurcations of Periodic Motion.- 2.4.4 Bifurcations — Changes of Stability in Periodic Motion.- 2.5 Modulation.- 2.5.1 The Role of Small Parameters.- 2.5.2 Running Mandelstam Lattices. Modulation of Waves by Waves.- 2.5.3 Generation of Modulation.- 2.5.4 Self-Modulation.- 2.5.5 Recurrence.- 2.5.6 Modulation Solitons.- 3. Chaos.- 3.1 Historical Remarks.- 3.2 Marble in an Oscillating Chute.- 3.3 Stochastic Self-Excited Oscillations.- 3.3.1 The Lorenz Attractor.- 3.3.2 Synchronization — Beats — Chaos.- 3.3.3 Autonomous Noise Generator.- 3.3.4 Scenarios for the Birth of Strange Attractors.- 3.4 Chaos and Noise.- 3.4.1 Dimension and Entropy.- 3.4.2 The Cantor Structure of a Strange Attractor.- 3.4.3 Dimension and Lyapunov Exponent.- 3.4.4 Deterministically Generated and Random Signals.- 4. Structures.- 4.1 Order and Disorder — Examples.- 4.2 Attractors and Spatial Patterns.- 4.2.1 Examples of Equations.- 4.2.2 Multistability. Defects.- 4.3 Self-Structures.- 4.3.1 Convective Self-Structures.- 4.3.2 Localization Mechanisms.- 4.3.3 Self-Structures in Three-Dimensional Media.- 4.3.4 Interaction of “Elementary Particles”.- 4.3.5 Birth and Interaction of Spiral Waves.- 4.4 Attractors — Memory — Learning.- 4.4.1 How to Remember.- 4.4.2 “Camera + TV + Feedback” Analogue.- 4.4.3 Critical Phenomena.- 4.4.4 Structures in Neuron-Like Media.- 5. Turbulence.- 5.1 Prehistory.- 5.2 Basic Models of Dynamic Theory.- 5.3 Turbulence and Structures in Two-Dimensional Fields.- 5.3.1 Experiments.- 5.3.2 Development of Turbulence and Multi-Dimensional Attractors.- 5.4 Spatial Evolution of Turbulence.- 5.4.1 Flow Dimension.- 5.4.2 Spatial Bifurcations.- 5.5 Discussion.- 6. Nonlinear Physics — Chaos and Order.- 6.1 The Where and the How.- 6.2 Randomness Born out of Nonrandomness.- 6.3 An Unstable Path and Steady Motion. Are They Incompatible?.- 6.4 Does Chance Rule the World?.- 6.5 What is the Character of Nature? Integer or Fractal?.- 6.6 Fractal Fingers.- 6.7 Self-Organizing Structures.- 6.8 Singles.- 6.9 The New Life of an Old Problem.- 6.10 Spatial Evolution of Disorder.- 6.11 What Does Your Camera See When It is Watching TV?.- 6.12 Multistability and Memory.- 6.13 Nonlinear Dynamics in Society.- Color Plates.- Literature.- Acknowledgements of the Figures.

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