Nonlinear oscillations and waves in dynamical systems:
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 w...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1996
|
| Schriftenreihe: | Mathematics and its applications
360 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | 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. 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. |
| Beschreibung: | XII, 538 S. graph. Darst. |
| ISBN: | 0792339312 |
Internformat
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| 245 | 1 | 0 | |a Nonlinear oscillations and waves in dynamical systems |c by P. S. Landa |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
| 300 | |a XII, 538 S. |b graph. Darst. | ||
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| 490 | 1 | |a Mathematics and its applications |v 360 | |
| 520 | 3 | |a 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. 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. | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a Oscillations | |
| 650 | 4 | |a Waves | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface xiii
Introduction 1
1 The purpose and subject matter of the book 1
2 The definition and significance of the theory of oscillations and waves.
The subject area of its investigations. The history of the creation
and development of this theory. The relation between the theory of
oscillations and waves and the problems of synergetics 3
Part I BASIC NOTIONS AND DEFINITIONS 7
Chapter 1 Dynamical systems. Phase space. Stochastic and chaotic
systems. The number of degrees of freedom 9
1.1 Definition of a dynamical system and its phase space 9
1.2 Classification of dynamical systems. The concept of energy 10
1.3 Integrable and non integrable systems. Action angle variables .... 13
1.4 Systems with slowly time varying parameters. Adiabatic invariants . 16
1.5 Dissipative systems. Amplifiers and generators 17
Chapter 2 Hamiltonian systems close to integrable. Appearance of
stochastic motions in Hamiltonian systems 19
2.1 The content of the Kolmogorov Arnold Moser theory 19
2.2 The Henon Heiles system 20
Chapter 3 Attractors and repellers. Reconstruction of attractors
from an experimental time series. Quantitative characteristics of
attractors 22
3.1 Simple and complex attractors and repellers. Stochastic and chaotic
attractors 22
3.2 Reconstruction of attractors from an experimental time series .... 24
3.3 Quantitative characteristics of attractors 25
Chapter 4 Natural and forced oscillations and waves. Self oscillations
and auto waves 28
4.1 Natural and forced oscillations and waves 28
vi
4.2 Self oscillations and auto waves 30
Part II BASIC DYNAMICAL MODELS OF THE
THEORY OF OSCILLATIONS AND WAVES 33
Chapter 5 Conservative systems 35
5.1 Harmonic oscillator 35
5.2 Anharmonic oscillator 36
5.3 The Lotka Volterra system ( prey predator model) 36
5.4 Chains of nonlinear oscillators. The Toda and Fermi Pasta Ulam
chains 37
5.5 The wave equation. The Klein Gordon and sine Gordon equations.
The Born Infeld equation 39
5.6 The equation of simple (Riemann) waves 41
5.7 The Boussinesq and Korteweg de Vries equations 43
5.8 The Whitham and Rudenko equations 50
5.9 The Khokhlov Zabolotskaya, cubic Schrodinger, Ginsburg Landau,
and Hirota equations 51
5.10 Some discrete models of conservative systems 56
Chapter 6 Non conservative Hamiltonian systems and dissipative
systems 58
6.1 Non linear damped oscillator with an external force 58
6.2 The Burgers and Burgers Korteweg de Vries equations 59
6.3 The van der Pol, Rayleigh, and Bautin equations 62
6.4 The equations of systems with inertial excitation and inertial
non linearity 62
6.5 The Lorenz, Rossler, and Chua equations 63
6.6 A model of an active string 65
6.7 Models for locally excited media(the equation for a kink wave, the
Fitz Hugh Nagumo and Turing equations) 65
6.8 The Kuramoto Sivashinsky equation 66
6.9 The Feigenbaum and Zisook maps 67
Part III NATURAL (FREE) OSCILLATIONS AND
WAVES IN LINEAR AND NON LINEAR SYSTEMS 69
Chapter 7 Natural oscillations of non linear oscillators 71
7.1 Pendulum oscillations 71
7.2 Oscillations described by the Duffing equation 72
7.3 Oscillations of a material point in a force field with the Toda potential 75
7.4 Oscillations of a bubble in fluid 77
7.5 Oscillations of species strength described by the Lotka Volterra
equations 81
vii
7.6 Oscillations in a system with slowly time varying natural frequency . 81
Chapter 8 Natural oscillations in systems of coupled oscillators 85
8.1 Linear conservative systems. Normal oscillations 85
8.2 Oscillations in linear homogeneous and periodically inhomogeneous
chains 87
8.3 Normal oscillations in non linear conservative systems 93
8.4 Oscillations in non linear homogeneous chains 99
8.5 Oscillations of coupled non linear damped oscillators. Homoclinic
structures. A model of acoustic emission 102
Chapter 9 Natural waves in bounded and unbounded continuous
media. Solitons 106
9.1 Normally and anomalously dispersive linear waves. Ionization waves
in plasmas. Planetary waves in ocean (Rossby waves and solitons) . . 106
9.2 Non linear waves described by the Born Infeld equation. Solitons of
the Klein Gordon and sine Gordon equations. Interaction between
solitons Ill
9.3 Simple, saw tooth and shock waves 116
9.4 Solitons of the Korteweg de Vries equation 121
9.5 Stationary waves described by the Burgers Korteweg de Vries equation 126
9.6 Solitons of the Boussinesq equation 126
9.7 Solitons of the cubic Schrodinger and Ginsburg Landau equations . . 127
9.8 Natural waves in slightly inhomogeneous and slightly non stationary
media. The wave action as an adiabatic invariant 129
9.9 Natural waves in periodically stratified media 133
Part IV FORCED OSCILLATIONS AND WAVES IN
PASSIVE SYSTEMS 137
Chapter 10 Oscillations of a non linear oscillator excited by an
external force 139
10.1 Periodically driven non linear oscillators. The main, subharmonic
and superharmonic resonances 139
10.1.1 The main resonance 141
10.1.2 Subharmonic resonances 144
10.1.3 Superharmonic resonances 146
10.2 Chaotic oscillations of non linear systems under periodic external
actions 147
10.2.1 Chaotic oscillations described by the Duffing equation 148
10.2.2 Chaotic oscillations of a gas bubble in liquid under the action
of a sound field 149
10.2.3 Chaotic oscillations in the Vallis model for non linear
interaction between ocean and atmosphere 149
viii
10.3 Oscillations excited by external force with a slowly time varying
frequency 152
Chapter 11 Oscillations of coupled non linear oscillators excited by an
external periodic force 156
11.1 The main resonance in a system of two coupled harmonically excited
non linear oscillators 156
11.2 Combination resonances in two coupled harmonically driven
non linear oscillators 161
11.3 Driven oscillations in linear homogeneous and periodically
inhomogeneous chains caused by a harmonic force applied to the input
of the chain 167
11.4 Forced oscillations in non linear homogeneous and periodically
inhomogeneous chains caused by a harmonic force applied to the input
of the chain. Excitation of the second harmonic and decay instability 173
11.5 Driven vibration of a string excited by a distributed external harmonic
force 184
Chapter 12 Parametric oscillations 186
12.1 Parametrically excited non linear oscillator 186
12.1.1 Slightly non linear oscillator with small damping and small
harmonic action 186
12.1.2 High frequency parametric action upon a pendulum.
Stabilization of the upper equilibrium position as an induced
phase transition 189
12.2 Chaotization of a parametrically excited non linear oscillator.
Regular and chaotic oscillations in a model of childhood infections
accounting for periodic seasonal change of the contact rate 191
12.3 Parametric resonances in a system of two coupled oscillators 192
12.4 Simultaneous forced and parametric excitation of a linear oscillator.
Parametric amplifier 199
Chapter 13 Waves in semibounded media excited by perturbations
applied to their boundaries 202
13.1 One dimensional waves in non linear homogeneous non dispersive
media. Shock and saw tooth waves 202
13.2 One dimensional waves in non linear homogeneous slightly dispersive
media described by the Korteweg de Vries equation 206
13.3 One dimensional waves in non linear highly dispersive media 206
13.4 Non linear wave bundles in dispersive media 211
13.4.1 Self focusing and self defocusing of wave bundles 211
13.4.2 Compression and expantion of pulses in non linear dispersive
media 216
13.5 Non linear wave bundles in non dispersive media. Approximate
solutions of the Khokhlov Zabolotskaya equation 218
13.6 Waves in slightly inhomogeneous media 220
ix
13.7 Waves in periodically inhomogeneous media 223
Part V OSCILLATIONS AND WAVES IN
ACTIVE SYSTEMS. SELF OSCILLATIONS AND
AUTO WAVES 225
Chapter 14 Forced oscillations and waves in active non self oscillatory
systems. Turbulence. Burst instability. Excitation of waves with
negative energy 227
14.1 Amplifiers with lumped parameters 227
14.2 Continuous semibounded media with convective instability 228
14.3 Excitation of turbulence in non closed fluid flows. The Klimontovich
criterion of motion ordering 229
14.4 One dimensional waves in active non linear media. Burst instability . 232
14.5 Waves with negative energy and instability caused by them 235
Chapter 15 Mechanisms of excitation and amplitude limitation of
self oscillations and auto waves. Classification of self oscillatory
systems 239
15.1 Mechanisms of excitation and amplitude limitation of self oscillations
in the simplest systems. Soft and hard excitation of self oscillations . 239
15.2 Mechanisms of the excitation of self oscillations in systems with high
frequency power sources 241
15.3 Mechanisms of excitation of self oscillations in continuous systems.
Absolute instability as a mechanism of excitation of auto waves . . . 242
15.4 Quasi harmonic and relaxation self oscillatory systems. Stochastic
and chaotic systems 242
15.5 Possible routes for loss of stability of regular motions and the
appearance of chaos and stochastieity 243
15.5.1 The Feigenbaum scenario 243
15.5.2 The transition to chaos via fusion of a stable limit cycle with
an unstable one and the subsequent disappearance of both of
these cycles 244
15.5.3 The transition to chaos via destruction of a two dimensional
torus 244
15.5.4 The Ruelle Takens scenario 245
Chapter 16 Examples of self oscillatory systems with lumped
parameters. I 246
16.1 Electronic generator. The van der Pol and Rayleigh equations .... 246
16.2 The Kaidanovsky Khaikin frictional generator and the Fronde
pendulum 250
16.3 The Bonhoeffer van der Pol oscillator 252
16.4 A model of glycolysis and a lumped version of the brusselator .... 253
16.5 A lumped model of the Buravtsev oscillator 256
X
16.6 Clock movement mechanisms and the Neimark pendulum. The
energetic criterion of self oscillation chaotization 259
16.7 Self oscillatory models for species interaction based on the
Lotka Volterra equations 263
16.8 Systems with inertial non linearity 264
16.8.1 The Pikovsky model 267
16.9 Systems with inertial excitation 267
16.9.1 The Helmholtz resonator with non uniformly heated walls . . 270
16.9.2 A heated wire with a weight at its centre 272
16.9.3 A modified brusselator 276
16.9.4 Self oscillations of an air cushioned body 277
Chapter 17 Examples of self oscillatory systems with lumped
parameters. II 283
17.1 The Rossler and Chua systems 283
17.2 A three dimensional model of an immune reaction illustrating an
oscillatory course of some chronic diseases. The oregonator model . 284
17.3 The simplest model of the economic progress of human society .... 288
17.4 Models of the vocal source 293
17.5 A lumped model of the singing flame 303
Chapter 18 Examples of self oscillatory systems with high frequency
power sources 307
18.1 The Duboshinsky pendulum, a gravitational machine , and the
Andreev hammer 307
18.2 The Bethenod pendulum, the Papaleksi effect, and the Rytov device . 313
18.3 Electro mechanical vibrators. Capacitance sensors of small
displacements 317
Chapter 19 Examples of self oscillatory systems with time delay 322
19.1 Biological controlled systems 322
19.1.1 Models of respiration control 323
19.1.2 The Mackey Glass model of the process of regeneration of
white blood corpuscles (neutrophils) 329
19.1.3 Models of the control of upright human posture 333
19.2 The van der Pol Duffing generator with additional delayed feedback
as a model of Doppler s autodyne 336
19.3 A ring optical cavity with an external field (the Ikeda system) .... 339
Chapter 20 Examples of continuous self oscillatory systems with
lumped active elements 341
20.1 The Vitt system. Competition and synchronization of modes 341
20.2 The Rijke phenomenon 348
20.3 A distributed model of the singing flame 351
xi
Chapter 21 Examples of self oscillatory systems with distributed
active elements 354
21.1 Lasers. Competition, synchronization and chaotization of modes.
Optical auto solitons 354
21.2 The Gann generators 368
21.3 Ionization waves (striations) in low temperature plasmas 374
21.3.1 Inert gases 378
21.3.2 Molecular gases 381
21.4 A model of the generation of Korotkov s sounds 384
21.5 Self oscillations of a bounded membrane resulting from excitation of
waves with negative energy 393
Chapter 22 Periodic actions on self oscillatory systems.
Synchronization and chaotization of self oscillations 396
22.1 Synchronization of periodic self oscillations by an external force in the
van der Pol Duffing generator. Two mechanisms of synchronization.
Synchronization as a non equilibrium phase transition 396
22.2 Synchronization of periodic oscillations in a generator with inertial
non linearity and in more complicated systems 401
22.3 Synchronization of a van der Pol generator with a modulated natural
frequency 404
22.4 Asynchronous quenching and asynchronous excitation of periodic
self oscillations 409
22.5 Chaotization of periodic self oscillations by a periodic external force .410
22.6 Synchronization of chaotic self oscillations. The synchronization
threshold and its relation to the quantitative characteristics of the
attractor 412
Chapter 23 Interaction between self oscillatory systems 414
23.1 Mutual synchronization of two generators of periodic oscillations . . .414
23.2 Mutual synchronization of three and more coupled generators of
periodic oscillations 421
23.3 Chaotization of self oscillations in systems of coupled generators . . . 423
23.4 Interaction between generators of periodic and chaotic oscillations . . 424
23.5 Interaction between generators of chaotic oscillations. The notion of
synchronization 426
Chapter 24 Examples of auto waves and dissipative structures 431
24.1 Auto waves of burning. A model of a kink wave 431
24.2 Auto waves in the Fitz Hugh Nagumo model 434
24.3 Auto waves in a distributed version of the brusselator and in some
other models of biological, chemical and ecological systems 436
24.4 Auto waves described by the Kuramoto Sivashinsky equation and the
generalized Kuramoto Sivashinsky equation 440
xii
Chapter 25 Convective structures and self oscillations in fluid. The
onset of turbulence 444
25.1 Rayleigh Taylor instability and the initial stage of the excitation of
thermo convection in a plane layer 444
25.2 Thermo convection in a toroidal tube. The Lorenz equations 451
25.3 The initial stage of excitation of bio convection 453
25.4 Onset of turbulence in the flow between two coaxial rotating cylinders.
Taylor vortices 456
Chapter 26 Hydrodynamic and acoustic waves in subsonic jet and
separated flows 463
26.1 The Kelvin Helmholtz instability 463
26.2 Subsonic free jets 465
26.3 Sound excitation by an impinging jet. Excitation of edgetones .... 477
26.4 Self oscillations in open jet return circuit wind tunnels 481
26.5 The von Karman vortex wake, Aeolian tones and stalling flutter . . . 486
Appendix A Approximate methods for solving linear differential
equations with slowly varying parameters 489
A.I JWKB Method 489
A.2 Asymptotic method 490
A.3 The Liouville Green transformation 491
A.4 The Langer transformation 492
Appendix B The Whitham method and the stability of periodic
running waves for the Klein Gordon equation 494
Bibliography 499
Index 535
|
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| id | DE-604.BV010744676 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:58:10Z |
| institution | BVB |
| isbn | 0792339312 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007175319 |
| oclc_num | 33983547 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-83 |
| owner_facet | DE-12 DE-384 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-83 |
| physical | XII, 538 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Landa, Polina S. Verfasser aut Nonlinear oscillations and waves in dynamical systems by P. S. Landa Dordrecht [u.a.] Kluwer 1996 XII, 538 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 360 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. 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. Nonlinear theories Oscillations Waves Nichtlineare Schwingung (DE-588)4042100-4 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Nichtlineare Schwingung (DE-588)4042100-4 s Dynamisches System (DE-588)4013396-5 s DE-604 Nichtlineare Welle (DE-588)4042102-8 s Mathematics and its applications 360 (DE-604)BV008163334 360 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007175319&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Landa, Polina S. Nonlinear oscillations and waves in dynamical systems Mathematics and its applications Nonlinear theories Oscillations Waves Nichtlineare Schwingung (DE-588)4042100-4 gnd Nichtlineare Welle (DE-588)4042102-8 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4042100-4 (DE-588)4042102-8 (DE-588)4013396-5 |
| title | Nonlinear oscillations and waves in dynamical systems |
| title_auth | Nonlinear oscillations and waves in dynamical systems |
| title_exact_search | Nonlinear oscillations and waves in dynamical systems |
| title_full | Nonlinear oscillations and waves in dynamical systems by P. S. Landa |
| title_fullStr | Nonlinear oscillations and waves in dynamical systems by P. S. Landa |
| title_full_unstemmed | Nonlinear oscillations and waves in dynamical systems by P. S. Landa |
| title_short | Nonlinear oscillations and waves in dynamical systems |
| title_sort | nonlinear oscillations and waves in dynamical systems |
| topic | Nonlinear theories Oscillations Waves Nichtlineare Schwingung (DE-588)4042100-4 gnd Nichtlineare Welle (DE-588)4042102-8 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Nonlinear theories Oscillations Waves Nichtlineare Schwingung Nichtlineare Welle Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007175319&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT landapolinas nonlinearoscillationsandwavesindynamicalsystems |