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E-grāmata: Chaos In Nature (Second Edition)

(Coria, Univ Of Rouen, France & Normandie Univ - Coria, France)
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Chaos In Nature (Second Edition)Palielināt
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This book is devoted to the history of chaos theory, from celestial mechanics (three-body problem) to electronics and meteorology. Many illustrative examples of chaotic behaviors exist in various contexts found in nature (chemistry, astrophysics, biomedicine). This book includes the most popular systems from chaos theory (Lorenz, Rössler, van der Pol, Duffing, logistic map, Lozi map, Hénon map etc.) and introduces many other systems, some of them very rarely discussed in textbooks as well as in scientific papers. The contents are formulated with an original approach as compared to other books on chaos theory.
Preface v
Foreword vii
Otto E. Rossler
Foreword ix
Robert Gilmore
Acknowledgments xi
From Celestial Mechanics to Chaos 1(74)
1 The Laws of Dynamics
3(8)
1.1 Kepler's Empirical Laws
3(3)
1.2 The Law of Gravitation
6(4)
1.3 Theory of the Moon
10(1)
2 The Three-Body Problem
11(8)
2.1 Imperfections in Newton's Theory
11(1)
2.2 Challenges to the Law of Gravitation
12(4)
2.3 Problem of the Convergence of Series
16(3)
3 Simplification of the Three-Body Problem
19(10)
3.1 Simplification of the Geometry
19(2)
3.2 Simplification of the General Equations
21(4)
3.3 The First Exact Solutions
25(4)
4 The Success of Celestial Mechanics
29(14)
4.1 Perturbation Theory
29(3)
4.2 The Theory of Jupiter and Saturn
32(1)
4.3 The Theory of the Moon
33(1)
4.4 Laplacian Determinism
34(3)
4.5 The Discovery of Neptune
37(3)
4.6 The Development of Perturbation Theory
40(3)
5 Birth of the Global Analysis
43(20)
5.1 The Restricted Three-Body Problem
43(3)
5.2 A Qualitative Analysis
46(2)
5.3 Studies of Sets of Solutions
48(2)
5.4 Dynamical Systems
50(1)
5.5 The Ideal Pendulum
50(3)
5.6 The Poincare-Bendixon Theorem
53(2)
5.7 Doubly Asymptotic Orbits
55(6)
5.8 Deterministic but Unpredictable
61(2)
6 The Stability of the Solar System
63(12)
6.1 The Problem of Small Divisors
64(1)
6.2 The KAM Theorem
65(3)
6.3 A Model for the KAM Theorem
68(4)
6.4 Numerical Approach
72(3)
Chaos in Nature: Properties and Examples 75(332)
1 Periodic and Chaotic Oscillators
77(12)
1.1 Oscillators and Degrees of Freedom
78(2)
1.2 Damped Pendulum
80(2)
1.3 Linear System of Two Oscillators
82(1)
1.4 Non-linear System of Two Oscillators
82(7)
2 From Mathematics to Electronic Circuits
89(72)
2.1 From Vacuum Tubes to Oscillating Circuits
90(7)
2.2 Dynamics of Various Oscillators
97(15)
2.2.1 The Colpitts Oscillation Circuit
97(2)
2.2.2 Synchronization between Distant Circuits
99(4)
2.2.3 The van der Pol Equation
103(5)
2.2.4 From Limit Cycle to more Complex Solutions
108(4)
2.3 Biological Systems as Electrical Circuits
112(10)
2.3.1 Simulations with Complex Electrical Circuits
112(5)
2.3.2 Simulations with the Simple van der Pol Equation
117(5)
2.4 From Electronics to Dynamical Systems
122(12)
2.4.1 The Hayashi's group
122(9)
2.4.2 The Toulouse Group
131(3)
2.5 Chaotic Electronic Circuits
134(15)
2.5.1 A Chaotic van der Pol Oscillator
134(2)
2.5.2 Chua's Zoo of Chaotic Circuits
136(13)
2.6 A van der Pol Oscillator for Describing Plasma Experiments
149(9)
2.6.1 Periodic Pulling in Q Machine
149(4)
2.6.2 A Chaotic Thermionic Diode
153(5)
2.7 Conclusion
158(3)
3 From Meteorology to Chaos: The Second Wave
161(28)
3.1 Prediction in Meteorology
161(5)
3.2 The Lorenz System
166(7)
3.2.1 State Space
167(2)
3.2.2 The Stability of Periodic Solutions
169(1)
3.2.3 Numerical Integration and Application of Linear Theory
170(1)
3.2.4 Topological Analysis
170(1)
3.2.5 First-return Map to Maxima
171(2)
3.3 Sensitivity to Initial Conditions
173(4)
3.4 Turbulence, Aperiodic Solutions, and Chaos
177(1)
3.5 Hydrodynamics and the Lorenz Attractor
178(2)
3.6 Laser Dynamics and the Lorenz System
180(5)
3.7 Conclusion
185(4)
4 The Architecture of Chaotic Attractors
189(56)
4.1 The Rossler System
189(24)
4.1.1 A Brief Biography
189(5)
4.1.2 Rossler's Main Influences
194(6)
4.1.3 A Chaotic Chemical Reaction
200(6)
4.1.4 The Rossler System
206(2)
4.1.5 A First Topological Analysis
208(5)
4.2 Poincare Section
213(1)
4.3 Symbolic Dynamics
214(4)
4.4 Characterization by Template as Periodic Orbits Holder
218(1)
4.5 A Simple Model for the Poincare Map
219(8)
4.6 Different Topologies for Chaos
227(12)
4.6.1 A Zoo of Chaotic Attractors
235(4)
4.7 Toroidal Chaos
239(4)
4.8 Conclusion
243(2)
5 Chemical Reactions
245(22)
5.1 The Earliest Experiments
245(5)
5.2 Chaos in an Experimental BZ-Reaction
250(8)
5.3 Chaotic Copper Electrodissolution
258(7)
5.4 Conclusion
265(2)
6 Population Evolution
267(20)
6.1 Theories of Malthus and Verhulst
267(4)
6.2 A Model with Two Species
271(4)
6.3 Models with Three Species
275(5)
6.4 Observational Evidence
280(7)
7 Chaotic Stars
287(46)
7.1 The Solar Activity
288(23)
7.1.1 Early Observations
288(7)
7.1.2 The Physics of the Sun
295(2)
7.1.3 A Model for the Solar Cycle
297(7)
7.1.4 A Global Model from the Sunspot Numbers
304(7)
7.2 Variable Stars
311(21)
7.2.1 Early Observations
311(11)
7.2.2 Hydrodynamical Models
322(8)
7.2.3 Observational Data
330(2)
7.3 Conclusion
332(1)
8 Chaos in Biology and Biomedicine
333(66)
8.1 Glycolysis Oscillations
333(4)
8.2 Fluctuations in Hematopoiesis
337(3)
8.3 Cardiac Arrhythmias
340(23)
8.3.1 The Beginnings of Electrophysiology
341(4)
8.3.2 The Heart - An Electric Machine
345(3)
8.3.3 Electrocardiograms and Arrhythmias
348(5)
8.3.4 Analysis of some Heart Rate Variability
353(10)
8.4 Patient Breathing with a Noninvasive Mechanical Ventilation
363(16)
8.4.1 Early Techniques for Mechanical Ventilation
363(3)
8.4.2 Lack of Synchronization between the Patient and His Device
366(4)
8.4.3 Breathing Variability under Mechanical Ventilation
370(9)
8.5 Dynamics of Tumor Growth
379(19)
8.5.1 The Model
382(2)
8.5.2 The Dynamics within a Single Site
384(4)
8.5.3 Spatial Tumor Growth
388(3)
8.5.4 Observability of Tumor Growth
391(7)
8.6 Conclusion
398(1)
9 Epilogue
399(8)
9.1 The Fourth Dimension
399(2)
9.2 A Weakly Dissipative System
401(1)
9.3 Another Toroidal Chaos
402(1)
9.4 Hyperchaotic Behavior
403(1)
9.5 Simple Models and Complex Behaviors
403(4)
General Index 407(6)
Author Index 413
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