Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boulder, Colorado
Westview Press
2015
|
| Ausgabe: | 2. edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 513 Seiten Illustrationen, Diagramme |
| ISBN: | 9780813349107 9780367092061 0813349109 |
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Datensatz im Suchindex
| _version_ | 1804151662661599232 |
|---|---|
| adam_text | Titel: Nonlinear dynamics and chaos
Autor: Strogatz, Steven
Jahr: 2015
CONTENTS Preface to the Second Edition ix Preface to the First Edition xi 1 Overview 1 1.0 Chaos, Fractals, and Dynamics 1 1.1 Capsule History of Dynamics 2 1.2 The Importance of Being Nonlinear 1.3 A Dynamical View of the World 9 Part I One-Dimensionc! Flows 2 Flows on the Line 15 2.0 Introduction 15 2.1 A Geometric Way of Thinking 16 2.2 Fixed Points and Stability 18 2.3 Population Growth 21 2.4 Linear Stability Analysis 24 2.5 Existence and Uniqueness 26 2.6 Impossibility of Oscillations 28 2.7 Potentials 30 2.8 Solving Equations on the Computer Exercises for Chapter 2 36 3 Bifurcations 45 3.0 Introduction 45 3.1 Saddle-Node Bifurcation 46 3.2 Transcritical Bifurcation 51 3.3 Laser Threshold 54 3.4 Pitchfork Bifurcation 56
3.5 Overdamped Bead on a Rotating Hoop 62 3.6 Imperfect Bifurcations and Catastrophes 70 3.7 Insect Outbreak 74 Exercises for Chapter 3 80 4 Flows on the Circle 95 4.0 Introduction 95 4.1 Examples and Definitions 95 4.2 Uniform Oscillator 97 4.3 Nonuniform Oscillator 98 4.4 Overdamped Pendulum 103 4.5 Fireflies 105 4.6 Superconducting Josephson Junctions 109 Exercises for Chapter 4 115 Part II Two-Dimensional Flows Linear Systems 125 5.0 Introduction 125 5.1 Definitions and Examples 125 5.2 Classification of Linear Systems 131 5.3 Love Affairs 139 Exercises for Chapter 5 142 Phase Plane 146 6.0 Introduction 146 6.1 Phase Portraits 146 6.2 Existence, Uniqueness, and Topological Consequences 149 6.3 Fixed Points and Linearization 151 6.4 Rabbits versus Sheep 156 6.5 Conservative Systems 160 6.6 Reversible Systems 164 6.7 Pendulum 168 6.8 Index Theory 174 Exercises for Chapter 6 181 Limit Cycles 198 7.0 Introduction 198 7.1 Examples 199 7.2 Ruling Out Closed Orbits 201 7.3 Poincare-Bendixson Theorem 205 7.4 Lienard Systems 212 7.5 Relaxation Oscillations 213
7.6 Weakly Nonlinear Oscillators 217 Exercises for Chapter 7 230 8 Bifurcations Revisited 244 8.0 Introduction 244 8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations 244 8.2 Hopf Bifurcations 251 8.3 Oscillating Chemical Reactions 257 8.4 Global Bifurcations of Cycles 264 8.5 Hysteresis in the Driven Pendulum and Josephson Junction 268 8.6 Coupled Oscillators and Quasiperiodicity 276 8.7 Poincare Maps 281 Exercises for Chapter 8 287 Part III Chaos 9 Lorenz Equations 309 9.0 Introduction 309 9.1 A Chaotic Waterwheel 310 9.2 Simple Properties of the Lorenz Equations 319 9.3 Chaos on a Strange Attractor 325 9.4 Lorenz Map 333 9.5 Exploring Parameter Space 337 9.6 Using Chaos to Send Secret Messages 342 Exercises for Chapter 9 348 10 One-Dimensional Maps 355 10.0 Introduction 355 10.1 Fixed Points and Cobwebs 356 10.2 Logistic Map: Numerics 360 10.3 Logistic Map: Analysis 364 10.4 Periodic Windows 368 10.5 Liapunov Exponent 373 10.6 Universality and Experiments 376 10.7 Renormalization 386 Exercises for Chapter 10 394 11 Fractals 405 11.0 Introduction 405 11.1 Countable and Uncountable Sets 406 11.2 Cantor Set 408 11.3 Dimension of Self-Similar Fractals 411 VII
11.4 Box Dimension 416 11.5 Pointwise and Correlation Dimensions 418 Exercises for Chapter 11 423 12 Strange Attractors 429 12.0 Introduction 429 12.1 The Simplest Examples 429 12.2 Henon Map 435 12.3 Rossler System 440 12.4 Chemical Chaos and Attractor Reconstruction 443 12.5 Forced Double-Well Oscillator 447 Exercises for Chapter 12 454 Answers to Selected Exercises 460 References 470 Author Index 483 Subject Index 487
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| any_adam_object | 1 |
| author | Strogatz, Steven 1959- |
| author_GND | (DE-588)128899816 |
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| classification_rvk | UG 3900 ST 300 |
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| discipline | Physik Informatik Mathematik |
| edition | 2. edition |
| format | Book |
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| spelling | Strogatz, Steven 1959- Verfasser (DE-588)128899816 aut Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering Steven H. Strogatz 2. edition Boulder, Colorado Westview Press 2015 XIII, 513 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Chemie (DE-588)4009816-3 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Technik (DE-588)4059205-4 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Biologie (DE-588)4006851-1 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s Chaostheorie (DE-588)4009754-7 s DE-604 Chaotisches System (DE-588)4316104-2 s Nichtlineares dynamisches System (DE-588)4126142-2 s Chaos (DE-588)4191419-3 s Physik (DE-588)4045956-1 s Biologie (DE-588)4006851-1 s Chemie (DE-588)4009816-3 s Technik (DE-588)4059205-4 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-0-8133-4911-4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026998329&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 |
| spellingShingle | Strogatz, Steven 1959- Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering Chemie (DE-588)4009816-3 gnd Physik (DE-588)4045956-1 gnd Chaotisches System (DE-588)4316104-2 gnd Technik (DE-588)4059205-4 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaostheorie (DE-588)4009754-7 gnd Biologie (DE-588)4006851-1 gnd Chaos (DE-588)4191419-3 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| subject_GND | (DE-588)4009816-3 (DE-588)4045956-1 (DE-588)4316104-2 (DE-588)4059205-4 (DE-588)4126142-2 (DE-588)4009754-7 (DE-588)4006851-1 (DE-588)4191419-3 (DE-588)4126141-0 |
| title | Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering |
| title_auth | Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering |
| title_exact_search | Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering |
| title_full | Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering Steven H. Strogatz |
| title_fullStr | Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering Steven H. Strogatz |
| title_full_unstemmed | Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering Steven H. Strogatz |
| title_short | Nonlinear dynamics and chaos |
| title_sort | nonlinear dynamics and chaos with applications to physics biology chemistry and engineering |
| title_sub | with applications to physics, biology, chemistry, and engineering |
| topic | Chemie (DE-588)4009816-3 gnd Physik (DE-588)4045956-1 gnd Chaotisches System (DE-588)4316104-2 gnd Technik (DE-588)4059205-4 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaostheorie (DE-588)4009754-7 gnd Biologie (DE-588)4006851-1 gnd Chaos (DE-588)4191419-3 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| topic_facet | Chemie Physik Chaotisches System Technik Nichtlineares dynamisches System Chaostheorie Biologie Chaos Nichtlineare Dynamik |
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