Chaotic dynamics: an introduction
"Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. A...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. A special feature is the inclusion of both analytic and computer exercises with which the reader may expand upon the many numerical simulations included in the book. This allows learning through participation, without the extensive scientific background demanded by more advanced books." "This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. Experimental data from a chaotic pendulum are analyzed using methods of nonlinear time series analysis. With the help of new computer programs provided in the book (and also available from one of the authors on an optional diskette), readers and students can learn about these methods and use them to characterize their own data. The second edition also explains methods for short-term prediction and control. Spatio-temporal chaos is now introduced with examples from fluid dynamics, crystal growth, and other areas. The number of references has more than doubled; solutions are included to selected exercises." "This new edition of Chaotic dynamics can be used as a text for a unit on chaos for physics and engineering students at the second- and third-year level. Such a unit would fit very well into modern physics and classical mechanics courses."--BOOK JACKET. |
| Beschreibung: | XIV, 256 S. graph. Darst. |
| ISBN: | 9780521476850 0521471060 |
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Datensatz im Suchindex
| _version_ | 1804125168982818816 |
|---|---|
| adam_text | Contents
Preface page xi
Acknowledgments xiv
chapter one Introduction 1
chapter two Some helpful tools 7
2.1 Phase space 7
2.2 Poincare section 21
2.3 Spectral analysis of time series 27
Problems 35
chapter three Visualization of the pendulum s dynamics 39
3.1 Sensitivity to initial conditions 41
3.2 Phase diagrams and Poincare sections 43
3.3 Time series and power spectra 59
3.4 Basins of attraction 59
3.5 Bifurcation diagrams 66
Problems and simulations 72
chapter four Toward an understanding of chaos 74
4.1 The logistic map 76
4.1.1 Period doubling 77
4.1.2 The periodic windows 81
4.1.3 Lyapunov exponents 84
4.1.4 Entropy 86
4.1.5 Stretching and folding 88
4.2 The circle map 89
4.3 The horseshoe map 96
vii
viii Contents
4.4 Application to the pendulum 100
Problems 105
chapter five The characterization of chaotic attractors 109
5.1 Dimension 110
5.2 Lyapunov exponents 119
5.3 Lyapunov exponents and dimension 123
5.4 Information change and Lyapunov exponents 126
Problems 129
chapter six Experimental characterization, prediction, and
modification of chaotic states 133
6.1 Characterization of chaotic states 133
6.1.1 Experiment and simulation 135
6.1.2 Reconstruction of the attractor 137
6.1.3 Time delay coordinates 139
6.1.4 Choosing the time delay 143
6.1.5 Embedding dimension and attractor dimension 145
6.1.6 Lyapunov exponents 150
6.1.7 Summary 152
6.2 Prediction of chaotic states 152
6.2.1 Method of analogues 153
6.2.2 Linear approximation method 156
6.3 Modification of chaotic states 159
6.4 Conclusion 163
Problems 164
chapter seven Chaos broadly applied 166
7.1 Chaos in lasers 166
7.2 Chaotic chemical reactions 168
7.3 Chaos in fluid dynamics 170
7.4 Spatio temporal chaos in fluids 172
7.4.1 Spatio temporal chaos in thermal convection 173
7.4.2 Spatio temporal chaos on a rotating fluid film 176
7.5 Spatio temporal intermittency in model equations 178
7.6 Strong turbulence 179
7.7 Chaotic mixing in fluids 180
7.8 Complex dynamics of interfacial growth: artificial
snowflakes 181
7.9 Chaos in earthquake dynamics 184
7.10 Chaos and quantum physics 185
Contents ix
7.11 Foundations of statistical mechanics 187
7.12 Conclusion 189
Further reading 190
Appendix A Numerical integration
Runge Kutta method 193
Appendix B Computer program listings 196
Appendix C Solutions to selected problems 242
References 246
Index 253
Diskette order information 256
|
| any_adam_object | 1 |
| author | Baker, Gregory L. Gollub, Jerry P. |
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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | Baker, Gregory L. Verfasser aut Chaotic dynamics an introduction Gregory L. Baker and Jerry P. Gollub 2. ed. Cambridge [u.a.] Cambridge Univ. Press 1996 XIV, 256 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier "Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. A special feature is the inclusion of both analytic and computer exercises with which the reader may expand upon the many numerical simulations included in the book. This allows learning through participation, without the extensive scientific background demanded by more advanced books." "This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. Experimental data from a chaotic pendulum are analyzed using methods of nonlinear time series analysis. With the help of new computer programs provided in the book (and also available from one of the authors on an optional diskette), readers and students can learn about these methods and use them to characterize their own data. The second edition also explains methods for short-term prediction and control. Spatio-temporal chaos is now introduced with examples from fluid dynamics, crystal growth, and other areas. The number of references has more than doubled; solutions are included to selected exercises." "This new edition of Chaotic dynamics can be used as a text for a unit on chaos for physics and engineering students at the second- and third-year level. Such a unit would fit very well into modern physics and classical mechanics courses."--BOOK JACKET. Chaotic behavior in systems Pendulum Software (DE-588)4055382-6 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Dynamisches System (DE-588)4013396-5 s DE-604 Chaostheorie (DE-588)4009754-7 s Nichtlineares dynamisches System (DE-588)4126142-2 s 1\p DE-604 Chaos (DE-588)4191419-3 s 2\p DE-604 Dynamik (DE-588)4013384-9 s 3\p DE-604 Software (DE-588)4055382-6 s 4\p DE-604 Gollub, Jerry P. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007136158&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Baker, Gregory L. Gollub, Jerry P. Chaotic dynamics an introduction Chaotic behavior in systems Pendulum Software (DE-588)4055382-6 gnd Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaotisches System (DE-588)4316104-2 gnd Dynamisches System (DE-588)4013396-5 gnd Chaos (DE-588)4191419-3 gnd Dynamik (DE-588)4013384-9 gnd |
| subject_GND | (DE-588)4055382-6 (DE-588)4009754-7 (DE-588)4126142-2 (DE-588)4316104-2 (DE-588)4013396-5 (DE-588)4191419-3 (DE-588)4013384-9 |
| title | Chaotic dynamics an introduction |
| title_auth | Chaotic dynamics an introduction |
| title_exact_search | Chaotic dynamics an introduction |
| title_full | Chaotic dynamics an introduction Gregory L. Baker and Jerry P. Gollub |
| title_fullStr | Chaotic dynamics an introduction Gregory L. Baker and Jerry P. Gollub |
| title_full_unstemmed | Chaotic dynamics an introduction Gregory L. Baker and Jerry P. Gollub |
| title_short | Chaotic dynamics |
| title_sort | chaotic dynamics an introduction |
| title_sub | an introduction |
| topic | Chaotic behavior in systems Pendulum Software (DE-588)4055382-6 gnd Chaostheorie (DE-588)4009754-7 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaotisches System (DE-588)4316104-2 gnd Dynamisches System (DE-588)4013396-5 gnd Chaos (DE-588)4191419-3 gnd Dynamik (DE-588)4013384-9 gnd |
| topic_facet | Chaotic behavior in systems Pendulum Software Chaostheorie Nichtlineares dynamisches System Chaotisches System Dynamisches System Chaos Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007136158&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bakergregoryl chaoticdynamicsanintroduction AT gollubjerryp chaoticdynamicsanintroduction |