Dynamical chaos - models and experiments: appearance routes and structure of chaos in simple dynamical systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1995
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| Schriftenreihe: | [World scientific series on nonlinear science / A]
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 383 S. graph. Darst. |
| ISBN: | 9810221428 |
Internformat
MARC
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| 100 | 1 | |a Aniščenko, Vadim S. |d 1943- |e Verfasser |0 (DE-588)111580080 |4 aut | |
| 245 | 1 | 0 | |a Dynamical chaos - models and experiments |b appearance routes and structure of chaos in simple dynamical systems |c V. S. Anishchenko |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1995 | |
| 300 | |a XIV, 383 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804125178459848704 |
|---|---|
| adam_text | CONTENTS
Preface vii
Contents xi
Chapter 1. Stability and Bifurcation of
Dynamical Systems 1
1.1 Lineal analysis of stability. Variational equations 1
1.2 Spectrum of Lyapunov characteristic exponents of phase trajectories of
dynamical systems 2
1.3 Stability of equilibrium states 5
1.4 Stability of periodic solutions. Limit cycle multipliers 6
1.5 Stability of quasiperiodic and chaotic solutions 8
1.6 Discrete time systems. Poincare map 10
1.7 Stability of discrete system solutions 13
1.8 Structural stability and bifurcations 15
1.9 Bifurcation of equilibrium states 16
1.9.1 Bifurcation of codimension one a double equilibrium point 16
1.9.2 Bifurcation of codimension two a triple equilibrium point 17
1.9.3 Limit cycle birth bifurcation 18
1.9.4 Nonlocal codimension one bifurcations. The separatrix loop of saddle
equilibrium state 20
1.10 Bifurcations of periodic solutions 21
1.10.1 Saddle node bifurcation of limit cycle 22
1.10.2 Period doubling bifurcation of cycle 23
1.10.3 Two dimensional torus birth bifurcation 25
1.10.4 Symmetry breaking bifurcation 27
1.10.5 Nonlocal periodic motion bifurcations accompanied by a period
becoming infinite 29
1.11 Nonlocal bifurcations in the vicinity of double asymptotic trajectories 31
xi
xii Contents
Chapter 2. Numerical Methods of
Chaos Investigations 33
2.1 Experimental approach to investigation of nonlinear system dynamics 33
2.2 Calculation of the Poincare map 35
2.3 Numerical analysis of periodic solutions and their bifurcations 42
2.4 Numerical analysis of statistical properties of attractors 50
2.5 Algorithms for calculating the spectrum of Lyapunov characteristic exponents
(LCE) 55
2.6 Method of numerically calculating the singular solutions 60
2.7 Dimension calculating algorithms 64
Chapter 3. Inertial Nonlinearity Oscillator.
Regular Attractor Bifurcations 69
3.1 General equations of one and a half freedom degree oscillators 69
3.2 Statement of equations for a modified oscillator with inertial nonlinearity .... 73
3.3 Periodic oscillation regimes in the oscillator and their bifurcations under
variation of the parameters 79
3.3.1 Andronov Hopf bifurcation 80
3.3.2 Limit cycle bifurcations 83
Chapter 4. Autonomous Oscillation Regimes
in Oscillator 90
4.1 Two parametric analysis of transition to chaos via the cascade of period
doubling bifurcations 90
4.2 The Poincare map 96
4.3 System dynamics in the supercritical range of parameter values. Hysteresis
and transition to chaos via intermittency induced by fluctuations 104
4.4 Interaction of chaotic attractors. Intermittency of chaos chaos type 112
4.5 Dissipative nonlinearity influence on attractor bifurcations 116
Chapter 5. Quasiattractor Structure and
Properties and Homoclinic Trajectories of
Autonomous Oscillator 122
5.1 Oscillator dynamics in the vicinity of a homoclinic trajectory of saddle focus
separatrix loop type 122
5.2 Role of homoclinic saddle cycle trajectories in the chaotic attractor
bifurcations 131
5.3 Physical interpretation of exciting the nonperiodic oscillations in oscillator
with inertial nonlinearity 138
Contents xiii
5.4 On the dimension of an attractor 141
Chapter 6. Two Frequency Oscillation
Breakdown 146
6.1 General problem statement 146
6.2 Bifurcation diagram of nonautonomous oscillator in the vicinity of basic
resonance. Computer simulation 148
6.3 The bifurcation diagram of system (6.1). Full scale experiment 151
6.4 Two dimensional torus doubling bifurcation. Soft transition to chaos 155
6.5 Bifurcation mechanism of torus chaos birth under two frequency oscillation
breakdown 159
6.6 Universal quantitative regularities of soft transition to chaos via
two dimensional torus breakdown 164
Chapter 7. Breakdown of Two and
Three Frequency Quasiperiodic Oscillations 174
7.1 Transitions to torus chaos in the system of two coupled oscillators 174
7.2 Qualitative description of bifurcations in the system of coupled oscillators
by using a model map 180
7.3 Transitions to chaos via three frequency quasiperiodic oscillations 188
Chapter 8. Synchronization of Chaos 199
8.1 Introduction and definition of the problem 199
8.2 Experimental system and its mathematical model 200
8.3 Methods of investigation 203
8.4 Forced synchronization of chaos 205
8.5 Bifurcational mechanisms of synchronization in the region of chaos 210
8.6 Mutual synchronization of symmetrically coupled oscillators 211
8.7 Evolution of distribution density of phase spectra difference in the process of
synchronization 216
Chapter 9. Nonlinear Phenomena and
Chaos in Chua s Circuit 219
9.1 Definition of the problem 219
9.2 Chua s circuit 220
9.3 Chaos chaos intermittency and 1/f noise in Chua s circuit 231
9.4 Dynamics of non autonomous Chua s circuit 241
9.5 Stochastic resonance in Chua s circuit 248
9.6 Confirmation of the Afraimovich Shilnikov torus breakdown theorem via
Chua s torus circuit 255
xiv Contents
Chapter 10. Bifurcations of Dynamical System
in the Presence of Noise 268
10.1 Some methods of stochastic calculus 268
10.2 Influence of external noise on the bifurcations of equilibrium state 278
10.3 Period doubling bifurcations in the presence of noise 291
Chapter 11. Chaos Structure and Properties
in the Presence of Noise 302
11.1 Introduction 302
11.2 Regimes of dynamical chaos under the influence of noise
with finite intensity 304
11.3 Hyperbolic and quasihyperbolic attractors under the influence of
colored noise 308
11.4 Bifurcations of chaotic attractors in the presence of noise 312
11.5 Transitions in chaotic systems induced by noise 319
11.6 Statistical properties of intermittency in quasihyperbolic systems
in the presence of noise 325
Chapter 12. Reconstruction of Dynamical
Systems from Experimental Data 337
12.1 Introduction 337
12.2 Methods and algorithms 338
12.3 Results of map (12.1) reconstruction 342
12.4 Reconstruction of system (12.2) 345
12.5 Comparison of qualitative characteristics of reconstructed attractors with
original ones 350
12.6 Reconstruction of differential system 354
Bibliography 36i
Index 38i
|
| any_adam_object | 1 |
| author | Aniščenko, Vadim S. 1943- |
| author_GND | (DE-588)111580080 |
| author_facet | Aniščenko, Vadim S. 1943- |
| author_role | aut |
| author_sort | Aniščenko, Vadim S. 1943- |
| author_variant | v s a vs vsa |
| building | Verbundindex |
| bvnumber | BV010701167 |
| classification_rvk | SK 520 UG 3900 |
| ctrlnum | (OCoLC)260195511 (DE-599)BVBBV010701167 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV010701167 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:57:26Z |
| institution | BVB |
| isbn | 9810221428 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007142771 |
| oclc_num | 260195511 |
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| owner | DE-12 DE-384 DE-634 DE-11 DE-188 |
| owner_facet | DE-12 DE-384 DE-634 DE-11 DE-188 |
| physical | XIV, 383 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | World Scientific |
| record_format | marc |
| series2 | [World scientific series on nonlinear science / A] |
| spelling | Aniščenko, Vadim S. 1943- Verfasser (DE-588)111580080 aut Dynamical chaos - models and experiments appearance routes and structure of chaos in simple dynamical systems V. S. Anishchenko Singapore [u.a.] World Scientific 1995 XIV, 383 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [World scientific series on nonlinear science / A] 8 Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dissipatives System (DE-588)4209641-8 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Dynamisches System (DE-588)4013396-5 s DE-604 Dissipatives System (DE-588)4209641-8 s Chaostheorie (DE-588)4009754-7 s A] [World scientific series on nonlinear science 8 (DE-604)BV009051753 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007142771&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aniščenko, Vadim S. 1943- Dynamical chaos - models and experiments appearance routes and structure of chaos in simple dynamical systems Chaotisches System (DE-588)4316104-2 gnd Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd Dissipatives System (DE-588)4209641-8 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4009754-7 (DE-588)4013396-5 (DE-588)4209641-8 |
| title | Dynamical chaos - models and experiments appearance routes and structure of chaos in simple dynamical systems |
| title_auth | Dynamical chaos - models and experiments appearance routes and structure of chaos in simple dynamical systems |
| title_exact_search | Dynamical chaos - models and experiments appearance routes and structure of chaos in simple dynamical systems |
| title_full | Dynamical chaos - models and experiments appearance routes and structure of chaos in simple dynamical systems V. S. Anishchenko |
| title_fullStr | Dynamical chaos - models and experiments appearance routes and structure of chaos in simple dynamical systems V. S. Anishchenko |
| title_full_unstemmed | Dynamical chaos - models and experiments appearance routes and structure of chaos in simple dynamical systems V. S. Anishchenko |
| title_short | Dynamical chaos - models and experiments |
| title_sort | dynamical chaos models and experiments appearance routes and structure of chaos in simple dynamical systems |
| title_sub | appearance routes and structure of chaos in simple dynamical systems |
| topic | Chaotisches System (DE-588)4316104-2 gnd Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd Dissipatives System (DE-588)4209641-8 gnd |
| topic_facet | Chaotisches System Chaostheorie Dynamisches System Dissipatives System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007142771&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009051753 |
| work_keys_str_mv | AT aniscenkovadims dynamicalchaosmodelsandexperimentsappearanceroutesandstructureofchaosinsimpledynamicalsystems |