Nonlinear Oscillations and Waves in Dynamical Systems

✍ Scribed by P. S. Landa (auth.)

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Leaves: 550
• Series: Mathematics and Its Applications 360
• Edition: 1
• Category: Library

✦ Synopsis

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

✦ Table of Contents

Front Matter....Pages i-xv
Introduction....Pages 1-6
Front Matter....Pages 7-7
Dynamical systems. Phase space. Stochastic and chaotic systems. The number of degrees of freedom....Pages 9-18
Hamiltonian systems close to integrable. Appearance of stochastic motions in Hamiltonian systems....Pages 19-21
Attractors and repellers. Reconstruction of attractors from an experimental time series. Quantitative characteristics of attractors....Pages 22-27
Natural and forced oscillations and waves. Self-oscillations and auto-waves....Pages 28-31
Front Matter....Pages 33-33
Conservative systems....Pages 35-57
Non-conservative Hamiltonian systems and dissipative systems....Pages 58-67
Front Matter....Pages 69-69
Natural oscillations of non-linear oscillators....Pages 71-84
Natural oscillations in systems of coupled oscillators....Pages 85-105
Natural waves in bounded and unbounded continuous media. Solitons....Pages 106-136
Front Matter....Pages 137-137
Oscillations of a non-linear oscillator excited by an external force....Pages 139-155
Oscillations of coupled non-linear oscillators excited by an external periodic force....Pages 156-185
Parametric oscillations....Pages 186-201
Waves in semibounded media excited by perturbations applied to their boundaries....Pages 202-224
Front Matter....Pages 225-225
Forced oscillations and waves in active non-self-oscillatory systems. Turbulence. Burst instability. Excitation of waves with negative energy....Pages 227-238
Mechanisms of excitation and amplitude limitation of self-oscillations and auto-waves. Classification of self-oscillatory systems....Pages 239-245
Examples of self-oscillatory systems with lumped parameters. I....Pages 246-282
Examples of self-oscillatory systems with lumped parameters. II....Pages 283-306
Examples of self-oscillatory systems with high frequency power sources....Pages 307-321
Examples of self-oscillatory systems with time delay....Pages 322-340
Front Matter....Pages 225-225
Examples of continuous self-oscillatory systems with lumped active elements....Pages 341-353
Examples of self-oscillatory systems with distributed active elements....Pages 354-395
Periodic actions on self-oscillatory systems. Synchronization and chaotization of self-oscillations....Pages 396-413
Interaction between self-oscillatory systems....Pages 414-430
Examples of auto-waves and dissipative structures....Pages 431-443
Convective structures and self-oscillations in fluid. The onset of turbulence....Pages 444-462
Hydrodynamic and acoustic waves in subsonic jet and separated flows....Pages 463-488
Back Matter....Pages 489-544

✦ Subjects

Partial Differential Equations;Vibration, Dynamical Systems, Control;Mechanics;Acoustics;Biophysics and Biological Physics