Introduction to Nonlinear Dynamics for Physicists

By: H.D.I. Abarbanel, M. I. Rabinovich, Mikhail M. Sushchik

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Hardcover | 1 December 1992

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168 Pages

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This is a series of lecture notes on nonlinear dynamics for physicists. The level is that of an advanced undergraduate or beginning graduate student. The main aim of these lectures is to present a balance of qualitative and quantitative material. The book also aims to address three main questions about nonlinear dynamics: what is nonlinear dynamics all about and what makes it differ from linear dynamics which permeate all familiar textbooks?; from the physicist's point of view, why should we study nonlinear systems and leave the comfortable territory of linearity?; and how can one progress in the study of nonlinear systems both in the analysis of these systems when we know them, and in learning about new systems from observations of their experimental behaviour? As it would be impossible to answer these questions in the finest detail, this volume nevertheless points the way for the interested reader. Useful problems have also been incorporated as a guide.

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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

At a Glance

Hardcover

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