Nonlinear Oscillations and Waves in Dynamical Systems

ISBN-13: 9789048146703 / Angielski / Miękka / 2010 / 544 str.

P. S. Landa

Opis

This volume is an up-to-date treatment of the theory of nonlinear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified point of view. Also, the relation between the theory of oscillations and waves, nonlinear dynamics and synergetics is discussed. One of the purposes of this book is to convince readers of the necessity of a thorough study of the theory of oscillations and waves, and to show that such popular branches of science as nonlinear dynamics, and synergetic soliton theory, for example, are in fact constituent parts of this theory. Audience: This book will appeal to researchers whose work involves oscillatory and wave processes, and students and postgraduates interested in the general laws and applications of the theory of oscillations and waves.

Spis treści

Preface. Introduction. Part I: Basic Notions and Definitions. 1. Dynamical Systems. Phase Space. Stochastic and chaotic Systems. The Number of Degrees of Freedom. 2. Hamiltonian Systems Close to Integrable. Appearance of Stochastic Motions in Hamiltonian Systems. 3. Attractors and Repellers. Reconstruction of Attractors from an Experimental Time Series. Quantitative Characteristics of Attractors. 4. Natural and Forced Oscillations and Waves. Self-Oscillations and Auto-Waves. Part II: Basic Dynamical Models of the Theory of Oscillations and Waves. 5. Conservative Systems. 6. Non-Conservative Hamiltonian Systems and Dissipative Systems. Part III: Natural (Free) Oscillations and Waves in Linear and Non-Linear Systems. 7. Natural Oscillations of Non-Linear Oscillators. 8. Natural Oscillations in Systems of Coupled Oscillators. 9. Natural Waves in Bounded and Unbounded Continuous Media. Solitons. Part IV: Forced Oscillations and Waves in Passive Systems. 10. Oscillations of a Non-Linear Oscillator Excited by an External Force. 11. Oscillations of Coupled Non-linear Oscillators Excited by an External Periodic Force. 12. Parametric Oscillations. 13. Waves in Semibounded Media Excited by Perturbations Applied to their Boundaries. Part V: Oscillations and Waves in Active Systems. Self-Oscillations and Auto-Waves. 14. Forced Oscillations and Waves in Active Non-Self-Oscillatory Systems. Turbulence. Burst Instability. Excitation of Waves with Negative Energy. 15. Mechanisms of Excitation and Amplitude Limitation of Self-Oscillations and Auto-Waves. Classification of Self-Oscillatory Systems. 16. Examples of Self-Oscillatory Systems with Lumped Parameters. I. 17. Examples of Self-Oscillatory Systems with Lumped Parameters. II. 18. Examples of self-oscillatory Systems with High Frequency Power Sources. 19. Examples of Self-Oscillatory Systems with Time Delay. 20. Examples of Continuous Self-Oscillatory Systems with Lumped Active Elements. 21. Examples of Self-Oscillatory Systems with Distributed Active Elements. 22. Periodic Actions on Self-Oscillatory Systems. Synchronization and Chaotization of Self-Oscillations. 23. Interaction between Self-Oscillatory Systems. 24. Examples of Auto- Waves and Dissipative Structures. 25. Convective Structures and Self-Oscillations in Fluid. The Onset of Turbulence. 26. Hydrodynamic and Acoustic Waves in Subsonic Jet and Separated Flows. Appendix A: Approximate Methods for Solving Linear Differential Equations with Slowly Varying Parameters. Appendix B: The Whitham Method and the Stability of Periodic Running Waves for the Klein&endash;Gordon Equation. Bibliography. Index.