Foundations of Complex Systems : Nonlinear Dynamics, Statistical Physics, Information and Prediction

by Nicolis, Gregoire; Nicolis, Catherine

• ISBN13: 9789812700438
• ISBN10: 9812700439
• Format: Hardcover
• Copyright: 2007-09-03
• Publisher: Textstream

Summary

Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, how natural complexity acts as a source of inspiration for progress at the fundamental level.

Table of Contents

Preface	p. vii
The phenomenology of complex systems	p. 1
Complexity, a new paradigm	p. 1
Signatures of complexity	p. 3
Onset of complexity	p. 5
Four case studies	p. 8
Rayleigh-Benard convection	p. 8
Atmospheric and climatic variability	p. 11
Collective problem solving: food recruitment in ants	p. 15
Human systems	p. 19
Summing up	p. 23
Deterministic view	p. 25
Dynamical systems, phase space, stability	p. 25
Conservative systems	p. 27
Dissipative systems	p. 27
Levels of description	p. 34
The microscopic level	p. 34
The macroscopic level	p. 36
Thermodynamic formulation	p. 38
Bifurcations, normal forms, emergence	p. 41
Universality, structural stability	p. 46
Deterministic chaos	p. 49
Aspects of coupling-induced complexity	p. 53
Modeling complexity beyond physical science	p. 59
The probabilistic dimension of complex systems	p. 64
Need for a probabilistic approach	p. 64
Probability distributions and their evolution laws	p. 65
The retrieval of universality	p. 72
The transition to complexity in probability space	p. 77
The limits of validity of the macroscopic description	p. 82
Closing the moment equations in the mesoscopic description	p. 82
Transitions between states	p. 84
Average values versus fluctuations in deterministic chaos	p. 88
Simulating complex systems	p. 90
Monte Carlo simulation	p. 91
Microscopic simulations	p. 92
Cellular automata	p. 94
Agents, players and games	p. 95
Disorder-generated complexity	p. 96
Information, entropy and selection	p. 101
Complexity and information	p. 101
The information entropy of a history	p. 104
Scaling rules and selection	p. 106
Time-dependent properties of information. Information entropy and thermodynamic entropy	p. 115
Dynamical and statistical properties of time histories. Large deviations, fluctuation theorems	p. 117
Further information measures. Dimensions and Lyapunov exponents revisited	p. 120
Physical complexity, algorithmic complexity, and computation	p. 124
Summing up: towards a thermodynamics of complex systems	p. 128
Communicating with a complex system: monitoring, analysis and prediction	p. 131
Nature of the problem	p. 131
Classical approaches and their limitations	p. 131
Exploratory data analysis	p. 132
Time series analysis and statistical forecasting	p. 135
Sampling in time and in space	p. 138
Nonlinear data analysis	p. 139
Dynamical reconstruction	p. 139
Symbolic dynamics from time series	p. 143
Nonlinear prediction	p. 148
The monitoring of complex fields	p. 151
Optimizing an observational network	p. 153
Data assimilation	p. 157
The predictability horizon and the limits of modeling	p. 159
The dynamics of growth of initial errors	p. 160
The dynamics of model errors	p. 164
Can prediction errors be controlled?	p. 170
Recurrence as a predictor	p. 171
Formulation	p. 172
Recurrence time statistics and dynamical complexity	p. 176
Extreme events	p. 180
Formulation	p. 180
Statistical theory of extremes	p. 182
Signatures of a deterministic dynamics in extreme events	p. 185
Statistical and dynamical aspects of the Hurst phenomenon	p. 191
Selected topics	p. 195
The arrow of time	p. 195
The Maxwell-Boltzmann revolution, kinetic theory, Boltzmann's equation	p. 196
First resolution of the paradoxes: Markov processes, master equation	p. 200
Generalized kinetic theories	p. 202
Microscopic chaos and nonequilibrium statistical mechanics	p. 204
Thriving on fluctuations: the challenge of being small	p. 208
Fluctuation dynamics in nonequilibrium steady states revisited	p. 210
The peculiar energetics of irreversible paths joining equilibrium states	p. 211
Transport in a fluctuating environment far from equilibrium	p. 214
Atmospheric dynamics	p. 217
Low order models	p. 218
More detailed models	p. 222
Data analysis	p. 223
Modeling and predicting with probabilities	p. 224
Climate dynamics	p. 226
Low order climate models	p. 227
Predictability of meteorological versus climatic fields	p. 230
Climatic change	p. 233
Networks	p. 235
Geometric and statistical properties of networks	p. 236
Dynamical origin of networks	p. 239
Dynamics on networks	p. 244
Perspectives on biological complexity	p. 247
Nonlinear dynamics and self-organization at the biochemical, cellular and organismic level	p. 249
Biological superstructures	p. 251
Biological networks	p. 253
Complexity and the genome organization	p. 260
Molecular evolution	p. 263
Equilibrium versus nonequilibrium in complexity and self-organization	p. 267
Nucleation	p. 268
Stabilization of nanoscale patterns	p. 272
Supramolecular chemistry	p. 274
Epistemological insights from complex systems	p. 276
Complexity, causality and chance	p. 277
Complexity and historicity	p. 279
Complexity and reductionism	p. 283
Facts, analogies and metaphors	p. 285
Color plates	p. 287
Suggestions for further reading	p. 291
Index	p. 321
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