Chaotic Oscillators

Theory And Applications

By: Tomasz Kapitaniak (Editor)

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Hardcover | 1 November 1992

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668 Pages

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This volume brings together a comprehensive selection of over 50 reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behaviour in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection available.

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Introduction
Chaos before Chaos
Frequency Demultiplication	p. 4
On Nonlinear Differential Equations of the Second Order: I. The Equation [actual symbol not reproducible] - k(1 - y[superscript 2]) y + y = b[lambda]kcos([lambda]t + a), k Large	p. 6
Nonlinear Vibrations of a Buckled Beam under Harmonic Excitation	p. 16
Random Phenomena Resulting from Nonlinearity in the System Described by Duffing's Equation	p. 26
Description and Quantification of Chaotic Behavior
Strange Attractors	p. 40
Geometry from a Time Series	p. 52
Deterministic Representation of Chaos in Classical Dynamics	p. 57
Determining Lyapunov Exponents from a Time Series	p. 61
Analytical Methods
A Partial Differential Equation with Infinitely Many Periodic Orbits: Chaotic Oscillations of a Forced Beam	p. 98
Second Order Averaging and Bifurcations to Subharmonics in Duffing's Equation	p. 129
Subharmonic and Homoclinic Bifurcations in a Parametrically Forced Pendulum	p. 143
Power Spectra of Strange Attractors near Homoclinic Orbits	p. 156
The Mel'nikov's Technique for Highly Dissipative Systems	p. 160
The Variational Approach to the Theory of Subharmonic Bifurcations	p. 172
The Refined Approximate Criterion for Chaos in a Two-State Mechanical Oscillator	p. 198
Analytical Condition for Chaotic Behaviour of the Duffing Oscillator	p. 211
Classical Nonlinear Oscillators: Duffing, Van der Pol and Pendulum
Universal Scaling Property in Bifurcation Structure of Duffing's and of Generalized Duffing's Equations	p. 219
Superstructure in the Bifurcation Set of the Duffing's Equation, [actual symbol not reproducible] + dx + x + x[superscript 3] = f cos([omega]t	p. 224
On the Understanding of Chaos in Duffing's Equation Including a Comparison with Experiment	p. 229
Chaotically Transitional Phenomena in the Forced Negative-Resistance Oscillator	p. 234
Period-Doubling Cascades and Devil's Staircases of the Driven Van der Pol Oscillator	p. 242
Chaotic States and Routes to Chaos in the Forced Pendulum	p. 249
Josephson Junctions and Circle Maps	p. 263
Resonance and Symmetry Breaking for the Pendulum	p. 267
Other Oscillatory Systems
Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors	p. 289
Chaos after Period-Doubling Bifurcations in the Resonance of an Impact Oscillator	p. 296
Devil's Attractors and Chaos of a Driven Impact Oscillator	p. 300
A Periodically Forced Piecewise Linear Oscillator	p. 304
Complex Dynamics of Compliant Off-Shore Structures	p. 331
Chaos Generated by the Cutting Process	p. 352
The Stability of Modes at Rest in a Chaotic System	p. 355
Chaotic Motion of an Elastic-Plastic Beam	p. 366
Chua's Circuit Family	p. 371
Chaos via Torus Breakdown	p. 382
Chaos in Noisy Systems
Fluctuations and the Onset of Chaos	p. 401
Noise versus Chaos in Acousto-optic Bistability	p. 405
Generalized Multistability and Noise-Induced Jumps in a Nonlinear Dynamical System	p. 412
Chaotic Distribution of Non-Linear Systems Perturbed by Random Noise	p. 419
Influence of Perturbations on Period-Doubling Bifurcation	p. 423
Chaos In a Noisy Mechanical System with Stress Relaxation	p. 428
Homoclinic Chaos in Systems Perturbed by Weak Langevin Noise	p. 434
Strange Nonchaotic Attractors
Quasiperiodically Forced Dynamical Systems with Strange Nonchaotic Attractors	p. 452
Dimensions of Strange Nonchaotic Attractors	p. 470
Route to Chaos via Strange Non-chaotic Attractors	p. 476
Spatial Chaos
Chaos as a Limit in a Boundary Value Problem	p. 484
On the Connection between Statical and Dynamical Chaos	p. 488
Spatially Complex Equilibria of Buckled Rods	p. 494
Spatial Chaos and Localization Phenomena in Nonlinear Elasticity	p. 524
Soliton Chaos Models for Mechanical and Biological Elastic Chains	p. 530
Spatiotemporal Dynamics in a Dispersively Coupled Chain of Nonlinear Oscillators	p. 537
Fractal Basin Boundaries
Fractal Basin Boundaries	p. 548
Fractal Basin Boundaries and Homoclinic Orbit for Periodic Motion in a Two-Well Potential	p. 577
Fractal Basin Boundaries of an impacting Particle	p. 581
Integrity Measures Quantifying the Erosion of Smooth and Fractal Basins of Attraction	p. 588
References	p. 611
Table of Contents provided by Blackwell. All Rights Reserved.

Chaotic Oscillators

Theory And Applications

At a Glance

Hardcover

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Defective items

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