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Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers 2nd Revised edition [Pehme köide]

3.62/5 (41 hinnangut Goodreads-ist)
(Department of Physics and Astronomy, University of Nebraska-Lincoln)
  • Formaat: Paperback / softback, 672 pages, kõrgus x laius x paksus: 235x157x36 mm, kaal: 994 g, numerous figures and diagrams
  • Ilmumisaeg: 14-Sep-2000
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198507232
  • ISBN-13: 9780198507239
Teised raamatud teemal:
Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers 2nd Revised editionSuurem pilt
  • Formaat: Paperback / softback, 672 pages, kõrgus x laius x paksus: 235x157x36 mm, kaal: 994 g, numerous figures and diagrams
  • Ilmumisaeg: 14-Sep-2000
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198507232
  • ISBN-13: 9780198507239
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780198507239.html
Märksõnad:
Chaos and Nonlinear Dynamics introduces students, scientists, and engineers to the full range of activity in the rapidly growing field on nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a thorough treatment of both differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers). It is the only book at this level to include the increasingly important field of pattern formation and a survey of the controversial questions of quantum chaos. Important tools such as Lyapunov exponents and fractal dimensions are treated in detail. With over 200 figures and diagrams, and analytic and computer exercises for every chapter, the book can be used as a course-text or for self-instruction. This second edition has been restructured to make the book even more useful as a course text:many of the more complex examples and derivations have been moved to appendices. The extensive collection of annotated references has been updated through January 2000 and now includes listings of World Wide Web sites at many of the major nonlinear dynamics research centers. From reviews on the 1/e: 'What has been lacking is a single book that takes the reader with nothing but a knowledge of elementary calculus and physics all the way to the frontiers of research in chaos and nonlinear dynamics in all its facets. [ ...] a serious student, teacher, or researcher would be delighted to have this book on the shelf as a reference and as a window to the literature in this exciting and rapidly growing new field of chaos.' J.C. Sprott, American Journal of Physics, September 19944 'I congratulate the author on having managed to write an extremely thorough, comprehensive, and entertaining introduction to the fascinating field of nonlinear dynamics. His book is highly self- explanatory and ideally suited for self-instruction. There is hardly any question that the author does not address in an exceptionally readable manner. [ ...] I strongly recommend it to those looking for a comprehensive, practical, and not highly mathematical approach to the subject.' E.A. Hunt, IEEE Spectrum, December 1994
First Edition Preface v
First Edition Acknowledgments xi
Second Edition Preface xiii
Second Edition Acknowledgments xv
I. THE PHENOMENOLOGY OF CHAOS 1(68)
Three Chaotic Systems
3(44)
Prelude
3(1)
Linear and Nonlinear Systems
4(4)
A Nonlinear Electrical System
8(9)
A Mathematical Model of Biological Population Growth
17(10)
A Model of Convecting Fluids: The Lorenz Model
27(10)
Determinism, Unpredictability, and Divergence of Trajectories
37(2)
Summary and Conclusions
39(1)
Further Reading
40(7)
The Universality of Chaos
47(22)
Introduction
47(1)
The Feigenbaum Numbers
47(4)
Convergence Ratio for Real Systems
51(2)
Using δ to Make Predictions
53(2)
Feigenbaum Size Scaling
55(1)
Self-Similarity
56(1)
Other Universal Features
57(1)
Models and the Universality of Chaos
58(3)
Computers and Chaos
61(2)
Further Reading
63(1)
Computer Exercises
64(5)
II. TOWARD A THEORY OF NONLINEAR DYNAMICS AND CHAOS 69(248)
Dynamics in State Space: One and Two Dimensions
71(46)
Introduction
71(1)
State Space
72(2)
Systems Described by First-Order Differential Equations
74(3)
The No-Intersection Theorem
77(1)
Dissipative Systems and Attractors
78(1)
One-Dimensional State Space
79(4)
Taylor Series Linearization Near Fixed Points
83(1)
Trajectories in a One-Dimensional State Space
84(2)
Dissipation Revisited
86(1)
Two-Dimensional State Space
87(4)
Two-Dimensional State Space: The General Case
91(3)
Dynamics and Complex Characteristic Values
94(2)
Dissipation and the Divergence Theorem
96(1)
The Jacobian Matrix for Characteristic Values
97(3)
Limit Cycles
100(2)
Poincare Sections and the Stability of Limit Cycles
102(4)
Bifurcation Theory
106(7)
Summary
113(1)
Further Reading
114(2)
Computer Exercises
116(1)
Three-Dimensional State Space and Chaos
117(40)
Overview
117(1)
Heuristics
118(3)
Routes to Chaos
121(2)
Three-Dimensional Dynamical Systems
123(1)
Fixed Points in Three Dimensions
124(4)
Limit Cycles and Poincare Sections
128(6)
Quasi-Periodic Behavior
134(2)
The Routes to Chaos I: Period-Doubling
136(1)
The Routes to Chaos II: Quasi-Periodicity
137(1)
The Routes to Chaos III: Intermittency and Crises
138(1)
The Routes to Chaos IV: Chaotic Transients and Homoclinic Orbits
138(8)
Homoclinic Tangles and Horseshoes
146(2)
Lyapunov Exponents and Chaos
148(6)
Further Reading
154(1)
Computer Exercises
155(2)
Iterated Maps
157(53)
Introduction
157(1)
Poincare Sections and Iterated Maps
158(5)
One-Dimensional Iterated Maps
163(3)
Bifurcations in Iterated Maps: Period-Doubling, Chaos, and Lyapunov Exponents
166(7)
Qualitative Universal Behavior: The U-Sequence
173(10)
Feigenbaum Universility
183(2)
Tent Map
185(3)
Shift Maps and Symbolic Dynamics
188(4)
The Gaussian Map
192(5)
Two-Dimensional Iterated Maps
197(2)
The Smale Horseshoe Map
199(5)
Summary
204(1)
Further Reading
204(3)
Computer Exercises
207(3)
Quasi-Periodicity and Chaos
210(40)
Introduction
210(2)
Quasi-Periodicity and Poincare Sections
212(2)
Quasi-Periodic Route to Chaos
214(1)
Universality in the Quasi-Periodic Route to Chaos
215(2)
Frequency-Locking
217(1)
Winding Numbers
218(1)
Circle Map
219(8)
The Devil's Staircase and the Farey Tree
227(4)
Continued Fractions and Fibonacci Numbers
231(3)
On to Chaos and Universality
234(6)
Some Applications
240(6)
Further Reading
246(3)
Computer Exercises
249(1)
Intermittency and Crises
250(22)
Introduction
250(1)
What Is Intermittency?
250(2)
The Cause of Intermittency
252(4)
Quantitative Theory of Intermittency
256(3)
Types of Intermittency and Experimental Observations
259(1)
Crises
260(7)
Some Conclusions
267(1)
Further Reading
268(2)
Computer Exercises
270(2)
Hamiltonian Systems
272(45)
Introduction
272(1)
Hamilton's Equations and the Hamiltonian
273(3)
Phase Space
276(3)
Constants of the Motion and Integrable Hamiltonians
279(10)
Nonintegrable Systems, the KAM Theorem, and Period-Doubling
289(7)
The Henon-Heiles Hamiltonian
296(7)
The Chirikov Standard Map
303(5)
The Arnold Cat Map
308(1)
The Dissipative Standard Map
309(2)
Applications of Hamiltonian Dynamics
311(2)
Further Reading
313(3)
Computer Exercises
316(1)
III. MEASURES OF CHAOS 317(114)
Quantifying Chaos
319(56)
Introduction
319(1)
Time-Series of Dynamical Variables
320(3)
Lyapunov Exponents
323(4)
Universal Scaling of the Lyapunov Exponent
327(3)
Invariant Measure
330(5)
Kolmogorov-Sinai Entropy
335(6)
Fractal Dimension(s)
341(13)
Correlation Dimension and a Computational Case History
354(14)
Comments and Conclusions
368(1)
Further Reading
369(5)
Computer Exercises
374(1)
Many Dimensions and Multifractals
375(56)
General Comments and Introduction
375(1)
Embedding (Reconstruction) Spaces
376(7)
Practical Considerations for Embedding Calculations
383(6)
Generalized Dimensions and Generalized Correlation Sums
389(4)
Multifractals and the Spectrum of Scaling Indices f(α)
393(11)
Generalized Entropy and the g() Spectrum
404(9)
Characterizing Chaos via Periodic Orbits
413(2)
*Statistical Mechanical and Thermodynamic Formalism
415(5)
Wavelet Analysis, q-Calculus, and Related Topics
420(1)
Summary
421(1)
Further Reading
422(7)
Computer Exercises
429(2)
IV. SPECIAL TOPICS 431(102)
Pattern Formation and Spatiotemporal Chaos
433(57)
Introduction
433(3)
Two-Dimensional Fluid Flow
436(6)
Coupled-Oscillator Models, Cellular Automata, and Networks
442(8)
Transport Models
450(10)
Reaction-Diffusion Systems: A Paradigm for Pattern Formation
460(11)
Diffusion-Limited Aggregation, Dielectric Breakdown, and Viscous Fingering: Fractals Revisited
471(6)
Self-Organized Criticality: The Physics of Fractals?
477(2)
Summary
479(1)
Further Reading
480(9)
Computer Exercises
489(1)
Quantum Chaos, The Theory of Complexity, and Other Topics
490(43)
Introduction
490(1)
Quantum Mechanics and Chaos
490(18)
Chaos and Algorithmic Complexity
508(2)
Miscellaneous Topics: Piece-wise Linear Models, Time-Delay Models, Information Theory, Stochastic Resonance, Computer Networks, Controlling and Synchronizing Chaos
510(7)
Roll Your Own: Some Simple Chaos Experiments
517(1)
General Comments and Overview: The Future of Chaos
517(2)
Further Reading
519(14)
Appendix A: Fourier Power Spectra 533(8)
Appendix B: Bifurcation Theory 541(6)
Appendix C: The Lorenz Model 547(12)
Appendix D: The Research Literature on Chaos 559(1)
Appendix E: Computer Programs 560(8)
Appendix F: Theory of the Universal Feigenbaum Numbers 568(11)
Appendix G: The Duffing Double-Well Oscillator 579(5)
Appendix H: Other Universal Features for One-Dimensional Iterated Maps 584(5)
Appendix I: The van der Pol Oscillator 589(9)
Appendix J: Simple Laser Dynamics Models 598(7)
References 605(38)
Index 643


Robert C. Hilborn, Department of Physics and Astronomy, University of Nebraska-Lincoln