| 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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