Foundations of complex systems : nonlinear dynamics statistical physics and prediction / Gregoire Nicolis, Catherine Nicolis.

Format:

Book

Author/Creator:

Nicolis, G., 1939-

Contributor:

Nicolis, Cathy.

Language:

English

Subjects (All):

Complexity (Philosophy).

Nonlinear systems.

System analysis.

Computational complexity.

Nonlinear theories.

Physical Description:

xiv, 328 pages : illustrations ; 24 cm

Place of Publication:

Hackensack, N.J. : World Scientific, [2007]

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. Book jacket.

Contents:

1 The phenomenology of complex systems 1

1.1 Complexity, a new paradigm 1

1.2 Signatures of complexity 3

1.3 Onset of complexity 5

1.4 Four case studies 8

1.4.1 Rayleigh-Benard convection 8

1.4.2 Atmospheric and climatic variability 11

1.4.3 Collective problem solving: food recruitment in ants 15

1.4.4 Human systems 19

2 Deterministic view 25

2.1 Dynamical systems, phase space, stability 25

2.1.1 Conservative systems 27

2.1.2 Dissipative systems 27

2.2 Levels of description 34

2.2.1 The microscopic level 34

2.2.2 The macroscopic level 36

2.2.3 Thermodynamic formulation 38

2.3 Bifurcations, normal forms, emergence 41

2.4 Universality, structural stability 46

2.5 Deterministic chaos 49

2.6 Aspects of coupling-induced complexity 53

2.7 Modeling complexity beyond physical science 59

3 The probabilistic dimension of complex systems 64

3.1 Need for a probabilistic approach 64

3.2 Probability distributions and their evolution laws 65

3.3 The retrieval of universality 72

3.4 The transition to complexity in probability space 77

3.5 The limits of validity of the macroscopic description 82

3.5.1 Closing the moment equations in the mesoscopic description 82

3.5.2 Transitions between states 84

3.5.3 Average values versus fluctuations in deterministic chaos 88

3.6 Simulating complex systems 90

3.6.1 Monte Carlo simulation 91

3.6.2 Microscopic simulations 92

3.6.3 Cellular automata 94

3.6.4 Agents, players and games 95

3.7 Disorder-generated complexity 96

4 Information, entropy and selection 101

4.1 Complexity and information 101

4.2 The information entropy of a history 104

4.3 Scaling rules and selection 106

4.4 Time-dependent properties of information. Information entropy and thermodynamic entropy 115

4.5 Dynamical and statistical properties of time histories. Large deviations, fluctuation theorems 117

4.6 Further information measures. Dimensions and Lyapunov exponents revisited 120

4.7 Physical complexity, algorithmic complexity, and computation 124

4.8 Summing up: towards a thermodynamics of complex systems 128

5 Communicating with a complex system: monitoring, analysis and prediction 131

5.1 Nature of the problem 131

5.2 Classical approaches and their limitations 131

5.2.1 Exploratory data analysis 132

5.2.2 Time series analysis and statistical forecasting 135

5.2.3 Sampling in time and in space 138

5.3 Nonlinear data analysis 139

5.3.1 Dynamical reconstruction 139

5.3.2 Symbolic dynamics from time series 143

5.3.3 Nonlinear prediction 148

5.4 The monitoring of complex fields 151

5.4.1 Optimizing an observational network 153

5.4.2 Data assimilation 157

5.5 The predictability horizon and the limits of modeling 159

5.5.1 The dynamics of growth of initial errors 160

5.5.2 The dynamics of model errors 164

5.5.3 Can prediction errors be controlled? 170

5.6 Recurrence as a predictor 171

5.6.1 Formulation 172

5.6.2 Recurrence time statistics and dynamical complexity 176

5.7 Extreme events 180

5.7.1 Formulation 180

5.7.2 Statistical theory of extremes 182

5.7.3 Signatures of a deterministic dynamics in extreme events 185

5.7.4 Statistical and dynamical aspects of the Hurst phenomenon 191

6 Selected topics 195

6.1 The arrow of time 195

6.1.1 The Maxwell-Boltzmann revolution, kinetic theory, Boltzmann's equation 196

6.1.2 First resolution of the paradoxes: Markov processes, master equation 200

6.1.3 Generalized kinetic theories 202

6.1.4 Microscopic chaos and nonequilibrium statistical mechanics 204

6.2 Thriving on fluctuations: the challenge of being small 208

6.2.1 Fluctuation dynamics in nonequilibrium steady states revisited 210

6.2.2 The peculiar energetics of irreversible paths joining equilibrium states 211

6.2.3 Transport in a fluctuating environment far from equilibrium 214

6.3 Atmospheric dynamics 217

6.3.1 Low order models 218

6.3.2 More detailed models 222

6.3.3 Data analysis 223

6.3.4 Modeling and predicting with probabilities 224

6.4 Climate dynamics 226

6.4.1 Low order climate models 227

6.4.2 Predictability of meteorological versus climatic fields 230

6.4.3 Climatic change 233

6.5 Networks 235

6.5.1 Geometric and statistical properties of networks 236

6.5.2 Dynamical origin of networks 239

6.5.3 Dynamics on networks 244

6.6 Perspectives on biological complexity 247

6.6.1 Nonlinear dynamics and self-organization at the biochemical, cellular and organismic level 249

6.6.2 Biological superstructures 251

6.6.3 Biological networks 253

6.6.4 Complexity and the genome organization 260

6.6.5 Molecular evolution 263

6.7 Equilibrium versus nonequilibrium in complexity and self-organization 267

6.7.1 Nucleation 268

6.7.2 Stabilization of nanoscale patterns 272

6.7.3 Supramolecular chemistry 274

6.8 Epistemological insights from complex systems 276

6.8.1 Complexity, causality and chance 277

6.8.2 Complexity and historicity 279

6.8.3 Complexity and reductionism 283

6.8.4 Facts, analogies and metaphors 285.

Notes:

Includes bibliographical references and index.

ISBN:

9789812700438

9812700439

OCLC:

148662131