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Introduction To Nonlinear Dynamics For Physicists

By: Henry D I Abarbanel, Mikhail I Rabinovich, Mikhail M Sushchik

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Paperback | 1 June 1993

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168 Pages

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21.59 x 15.24 x 1.27

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This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.

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Non-Fiction Science Physics Classical Mathematics Science in General Maths for Scientists Mathematics Applied Mathematics Chaos Theory Booktopia Publisher Services World Scientific Publishing

Preface
Introduction	p. 1
Nonlinear Oscillator without Dissipation	p. 6
Equilibrium States of a Nonlinear Oscillator with Dissipation	p. 11
Oscillations Systems with Nonlinear Dissipation-Generators	p. 17
The Van der Pol Generator	p. 22
The Poincare Map	p. 27
Slow and Fast Motions in Systems with One Degree of Freedom	p. 33
Forced Nonlinear Oscillators: Linear and Nonlinear Resonances	p. 38
Forced Generator: Synchronization	p. 45
Competition of Modes	p. 51
Poincare Indices and Bifurcations of Equilibrium States	p. 55
Resonance Interactions between Oscillators	p. 62
Solitons	p. 69
Steady Propagation of Shock Waves	p. 80
Formation of Shock Waves	p. 86
Solitons. Shock Waves. Wave Interaction. The Spectral Approach	p. 89
Weak Turbulence. Random Phase Approximation	p. 95
Regular Patterns in Dissipative Media	p. 100
Deterministic Chaos. Qualitative Description	p. 104
Description of a Circuit with Chaos. Chaos in Maps	p. 111
Bifurcations of Periodic Motions. Period Doubling	p. 116
Controlled Nonlinear Oscillator. Intermittency	p. 122
Scenarios of the Onset of Chaos. Chaos through Quasi-Periodicity	p. 132
Characteristics of Chaos. Experimental Observation of Chaos	p. 139
Multidimensional Chaos. Discrete Ginzburg-Landau Model	p. 147
Problems to Accompany the Lectures	p. 151
Table of Contents provided by Blackwell. All Rights Reserved.

Introduction To Nonlinear Dynamics For Physicists

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Paperback

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