Applied chaos theory: a paradigm for complexity /

264 Pages·39.12 MB·English

by  A.B. Çambel.

APPLIED
CHAOS
THEORY
A PARADIGM FOR COMPLEXITY

APPLIED
CHAOS
THEORY
A PARADIGlv\ FOR COMPLEXITY
A. B. CA1\1BEL
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\C.\DEl\IIC PRFSS. IN<~.
l~!i() Sixth :\n·ntle, S;ul Diego, CA \12101-4:111
l 'nited Kingdom edition published hy
.\CADEl\IIC PRESS Ul\IITFD
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Lihrar\' of Congress Cataloging-in-l'nblication Data
(~amhd, :\li Bnlent. 19~:1.
Applied chaos theorv: ;1 p;1radigm for compll'xit\ A. B. (~amhel.
p. em.
Includes bibliographical rckrenrl's and index.
ISIIN 0-1~-15!1\l·Hl-K
I. ScietltT-l'hi losopln. 2. Compll'xitv (Philosophy) :1. Chaotic behador in systems.
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TABLE OF CONTENTS
Preface
XI
Acknowledgments
:.\'.V
1 living with Complexity
Introduction 1
Characteristics of Complexity 2
Laplace's Demon 7
~on linearity 8
A Sneak Pre\'iew of Chaos Theory 13
Degrees of Freedom and Numbers 17
Dynamical Systems 19
Scope 20
Quo Vndis? Reduction and Holism 22
:\otcs and Refcren(es 23
2 Meta-Quanitification of Complexity
Introduction ~~
Facing the 1\;ew Realitit>s :!R
vii
viii CONTENTS
Hierarchical Approa<"h 30
Geometric Approach 33
Algorithmic Complexity 35
Notes and References 38
3 The Anatomy of Systems and Structures
Introduction 41
Open, Closed, and Isolated Systems 41
Phase Space 44
Equilibrium and Nonequilibrium 47
Stability and Instability 48
Parameters to Evaluate Equilibrium 50
Rayleigh-Benard Instability 52
Irreversibility 54
Notes and References 57
4 Attractors
Introduction 59
Fixed-Point Attractors 61
Limit Cycles 64
Torus Attractors 69
Strange Attractors 69
Bernoulli Shift 74
Lyapunov Exponential ( :oefficient 76
Belousov-Zhabotinsky Reaction 77
Notes and References 79
5 Rapid Growth
Introduction HI
Malthus's Theory and the Exponential Equation H2
Fibonacci Series H6
Notes and References 89
6 The Logistic Curve
Introduction
Verhulst's Equation
Clues f(>r Technological R&D Planning
CONTENTS ix
Lotka-\ oltt rra I:quation:-
.:\ote:-- and Rt·ft>JTnet·:- 1( )()
7 The Discrete Logistic Equation
1n trod uction 107
The Discrete Logistic Curve 10!1
The ~lorpholog) of the Disn·t>te Lo~i:--til Equation 111
R<.>turn ~lap:-- 1 1~
Bifurcation Diagr.un 117
Feigenbaum Cni,·crsal ;\umbers 121
~1 ul tivariable Equations 124
~ ot<.>s and References l~-4
8 The Different Personalities of Entropy
In tTorluction 127
Is F.ntrnpy for Rt>al? 129
Why ~lucid\' the Waters with Entropy? I:)( I
\lacroscopic Entropy 1~ ~:~
Statistical Entropy l-41
Dynamic En tropit s 1:'11
:'-.'otes and References 157
9 Dimensions and Scaling
In trorluction 1G 1
Dimensiuns 16-4
Ha us do rtf -Bes inwi tc l1 D i1nen si01 1 1():-J
E.mlwrlding Dimension 167
Scaling 1{ )9
:'-." otes ,m d References 1 7:~
10 Gallery of Monsters
lntn1dunion 1/ ;-,
Bat kgwund lib
.Juli.l aod \!andclhn •t ~cts I~
Barn,Jn 's ( hao' t .,\llll 1~:--.
\.'ott'' and Rcfl·rcJll 11
t'"
X CONTENTS
11 The Diagnostics and Control of Chaos
Introduction 193
Time Series 195
Time Series Analysis 199
Log-Normal Distribution and 1/f Noise 204
Ising Model 207
Chaos Diagnostics 208
Chaos Control 215
Start Your Own Chaos Laboratory 217
Notes and References 220
12 Discussion Topics 223
Index of Names 235
Subject Index 241