Chaotic transitions in deterministic and stochastic dynamical systems:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2002
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Schriftenreihe: | Princeton series in applied mathematics
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XIV, 224 S. Ill., graph. Darst. |
ISBN: | 0691050945 |
Internformat
MARC
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245 | 1 | 0 | |a Chaotic transitions in deterministic and stochastic dynamical systems |c Emil Simiu |
264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2002 | |
300 | |a XIV, 224 S. |b Ill., graph. Darst. | ||
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650 | 0 | 7 | |a Stochastisches dynamisches System |0 (DE-588)4305316-6 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Chaotisches System |0 (DE-588)4316104-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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adam_text | Contents
Preface xi
Chapter 1. Introduction 1
PART 1. FUNDAMENTALS 9
Chapter 2. Transitions in Deterministic Systems and the Melnikov Function 11
2.1 Flows and Fixed Points. Integrable Systems. Maps: Fixed and
Periodic Points 13
2.2 Homoclinic and Heteroclinic Orbits. Stable and Unstable Manifolds 20
2.3 Stable and Unstable Manifolds in the Three Dimensional Phase
Space {jcl7 x2, t] 23
2.4 The Melnikov Function 27
2.5 Melnikov Functions for Special Types of Perturbation. Melnikov
Scale Factor 29
2.6 Condition for the Intersection of Stable and Unstable Manifolds.
Interpretation from a System Energy Viewpoint 36
2.7 Poincare Maps, Phase Space Slices, and Phase Space Flux 38
2.8 Slowly Varying Systems 45
Chapter 3. Chaos in Deterministic Systems and the Melnikov Function 51
3.1 Sensitivity to Initial Conditions and Lyapounov Exponents. Attractors
and Basins of Attraction 52
3.2 Cantor Sets. Fractal Dimensions 57
3.3 The Smale Horseshoe Map and the Shift Map 59
3.4 Symbolic Dynamics. Properties of the Space 22 Sensitivity to Initial
Conditions of the Smale Horseshoe Map. Mathematical Definition
of Chaos 65
3.5 Smale Birkhoff Theorem. Melnikov Necessary Condition for Chaos.
Transient and Steady State Chaos 67
3.6 Chaotic Dynamics in Planar Systems with a Slowly Varying Parameter 70
3.7 Chaos in an Experimental System: The Stoker Column 71
Chapter 4. Stochastic Processes 76
4.1 Spectral Density, Autocovariance, Cross Covariance 76
4.2 Approximate Representations of Stochastic Processes 87
4.3 Spectral Density of the Output of a Linear Filter with Stochastic Input 94
Viii CONTENTS
Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the
Melnikov Process 98
5.1 Behavior of a Fluidelastic Oscillator with Escapes: Experimental and
Numerical Results 100
5.2 Systems with Additive and Multiplicative Gaussian Noise: Melnikov
Processes and Chaotic Behavior 102
5.3 Phase Space Flux 106
5.4 Condition Guaranteeing Nonoccurrence of Escapes in Systems Excited
by Finite Tailed Stochastic Processes. Example: Dichotomous Noise 109
5.5 Melnikov Based Lower Bounds for Mean Escape Time and for
Probability of Nonoccurrence of Escapes during a Specified
Time Interval 112
5.6 Effective Melnikov Frequencies and Mean Escape Time 119
5.7 Slowly Varying Planar Systems 122
5.8 Spectrum of a Stochastically Forced Oscillator: Comparison between
Fokker Planck and Melnikov Based Approaches 122
PART 2. APPLICATIONS 127
Chapter 6. Vessel Capsizing 129
6.1 Model for Vessel Roll Dynamics in Random Seas 129
6.2 Numerical Example 132
Chapter 7. Open Loop Control of Escapes in Stochastically Excited Systems 134
7.1 Open Loop Control Based on the Shape of the Melnikov Scale Factor 134
7.2 Phase Space Flux Approach to Control of Escapes Induced by
Stochastic Excitation 140
Chapter 8. Stochastic Resonance 144
8.1 Definition and Underlying Physical Mechanism of Stochastic
Resonance. Application of the Melnikov Approach 145
8.2 Dynamical Systems and Melnikov Necessary Condition for Chaos 146
8.3 Signal to Noise Ratio Enhancement for a Bistable Deterministic System 147
8.4 Noise Spectrum Effect on Signal to Noise Ratio for Classical Stochastic
Resonance 149
8.5 System with Harmonic Signal and Noise: Signal to Noise Ratio
Enhancement through the Addition of a Harmonic Excitation 152
8.6 Nonlinear Transducing Device for Enhancing Signal to Noise Ratio 153
8.7 Concluding Remarks 155
Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a
First Order Dynamical System 156
9.1 Introduction 156
9.2 Transformed Equation Excited by White Noise 157
CONTENTS ix
Chapter 10. Snap Through of Transversely Excited Buckled Column 159
10.1 Equation of Motion 160
10.2 Harmonic Forcing 161
10.3 Stochastic Forcing. Nonresonance Conditions. Melnikov Processes for
Gaussian and Dichotomous Noise 163
10.4 Numerical Example 164
Chapter 11. Wind Induced Along Shore Currents over a Corrugated Ocean Floor 167
11.1 Offshore Flow Model 168
11.2 Wind Velocity Fluctuations and Wind Stresses 170
11.3 Dynamics of Unperturbed System 172
11.4 Dynamics of Perturbed System 173
11.5 Numerical Example 174
Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System 178
12.1 Experimental Neurophysiological Results 179
12.2 Results of Simulations Based on the Fitzhugh Nagumo Model.
Comparison with Experimental Results 182
12.3 Asymmetric Bistable Model of Auditory Nerve Fiber Response 183
12.4 Numerical Simulations 186
12.5 Concluding Remarks 190
Appendix A1 Derivation of Expression for the Melnikov Function 191
Appendix A2 Construction of Phase Space Slice through Stable and
Unstable Manifolds 193
Appendix A3 Topological Conjugacy 199
Appendix A4 Properties of Space 22 201
Appendix A5 Elements of Probability Theory 203
Appendix A6 Mean Upcrossing Rate t 1 for Gaussian Processes 211
Appendix A7 Mean Escape Rate t~ for Systems Excited by White Noise 213
References 215
Index 221
|
any_adam_object | 1 |
author | Simiu, Emil |
author_facet | Simiu, Emil |
author_role | aut |
author_sort | Simiu, Emil |
author_variant | e s es |
building | Verbundindex |
bvnumber | BV014308657 |
classification_rvk | SK 820 |
ctrlnum | (OCoLC)633304917 (DE-599)BVBBV014308657 |
discipline | Mathematik |
format | Book |
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id | DE-604.BV014308657 |
illustrated | Illustrated |
indexdate | 2024-07-09T19:01:26Z |
institution | BVB |
isbn | 0691050945 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009815797 |
oclc_num | 633304917 |
open_access_boolean | |
owner | DE-355 DE-BY-UBR |
owner_facet | DE-355 DE-BY-UBR |
physical | XIV, 224 S. Ill., graph. Darst. |
publishDate | 2002 |
publishDateSearch | 2002 |
publishDateSort | 2002 |
publisher | Princeton Univ. Press |
record_format | marc |
series2 | Princeton series in applied mathematics |
spelling | Simiu, Emil Verfasser aut Chaotic transitions in deterministic and stochastic dynamical systems Emil Simiu Princeton [u.a.] Princeton Univ. Press 2002 XIV, 224 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Princeton series in applied mathematics Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Stochastisches dynamisches System (DE-588)4305316-6 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Stochastisches dynamisches System (DE-588)4305316-6 s Chaotisches System (DE-588)4316104-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009815797&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Simiu, Emil Chaotic transitions in deterministic and stochastic dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd Stochastisches dynamisches System (DE-588)4305316-6 gnd Chaotisches System (DE-588)4316104-2 gnd |
subject_GND | (DE-588)4137931-7 (DE-588)4305316-6 (DE-588)4316104-2 |
title | Chaotic transitions in deterministic and stochastic dynamical systems |
title_auth | Chaotic transitions in deterministic and stochastic dynamical systems |
title_exact_search | Chaotic transitions in deterministic and stochastic dynamical systems |
title_full | Chaotic transitions in deterministic and stochastic dynamical systems Emil Simiu |
title_fullStr | Chaotic transitions in deterministic and stochastic dynamical systems Emil Simiu |
title_full_unstemmed | Chaotic transitions in deterministic and stochastic dynamical systems Emil Simiu |
title_short | Chaotic transitions in deterministic and stochastic dynamical systems |
title_sort | chaotic transitions in deterministic and stochastic dynamical systems |
topic | Differenzierbares dynamisches System (DE-588)4137931-7 gnd Stochastisches dynamisches System (DE-588)4305316-6 gnd Chaotisches System (DE-588)4316104-2 gnd |
topic_facet | Differenzierbares dynamisches System Stochastisches dynamisches System Chaotisches System |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009815797&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT simiuemil chaotictransitionsindeterministicandstochasticdynamicalsystems |