Exploring Complexity An Introduction

includes index and biblioraphy

COMPLEXITY IN NATURE 5 1.I What is complexity? 6 1.2 Self-organization in physico-chemical systems: the birth of complexity 8 1.3 Thermal convection, a prototype of self-organization phenomena in physics 8 1.4 Self-organization phenomena in chemistry 15 1.5 Physico-chemical complexity and algorithmic complexity 26 1.6 Some further examples of complex behavior on our scale 28 1.7 Again, biological systems 31 1.8 Complexity at the planetary and the cosmic scale 36 1.9 Forces versus correlations-a summing up 41 THE VOCABULARY OF COMPLEXITY 45 2.1 Conservative systems 46 2.2 Dissipative systems 50 2.3 Mechanical and thermodynamic equilibrium. Nonequilibrium constraints 54 2.4 Nonlinearity and feedbacks 56 2.5 The many facets of the second law 61 2.6 Stability 65 2.7 Bifuraction and symmetry breaking 71 2.8 Order and correlations 75 3 DYNAMICAL SYSTEMS AND COMPLEXITY 79 3.1 The geometry of phase space 80 3.2 Measures in phase space 82 3.3 Integrable conservative systems 88 3.4 Bifurcation in simple dissipative systems: search for archetypes of complexity 3.5 Dissipative systems in two-dimensional phase spaces: limit cycles 98 3.6 Reduction to low-dimensional systems: order parameters and normal forms 103 3.7 Phase space revisited: topological manifolds and fractals 110 3.8 Nonintegrable conservative systems: the new mechanics 715 3.9 A model of unstable motion: the horseshoe 121 3.10 Dissipative systems in multidimensional phase spaces. Chaos and strange attractors 123 3.11 Spatially distributed systems. Symmetry-breaking bifurcations and morphogenesis 132 3.12 Discrete dynamical systems. Cellular automata 138 3.13 Asymmetry, selection, and information 141 4 RANDOMNESS AND COMPLEXITY 147 4.1 Fluctuations and probabilistic description 148 4.2 Markov processes. Master equation 153 4.3 Markov processes and irreversibility. Information entropy and physical entropy 4.4 Spatial correlations and critical behavior 164 4.5 Time-dependent behavior of the fluctuations. The kinetics and the time scales of self-organization 171 4.6 Sensitivity and selection 179 4.7 Symbolic dynamics and information 183 4.8 Generation of asymmetric, information-rich structures 186 4.9 Once again, algorithmic complexity 191 5 TOWARD A UNIFIED FORMULATION OF COMPLEXITY 193 5.1 General properties of conserved dynamical systems 194 5.2 General properties of dissipative dynamical systems 197 5.3 The search for unification 198 5.4 Probability and dynamics 199 5.5 The Baker transformation 200 5.6 Manifolds with broken time symmetry 204 5.7 The symmetry-breaking transformation A 205 5.8 Gibbs ensembles and Boltzmann ensembles 209 5.9 Kinetic theory 210 5.10 Resonance and light-matter interaction 272 5.ll Concluding remarks 274 COMPLEXITY AND THE TRANSFER OF KNOWLEDGE 217 6.1 Nonlinear dynamics in far-from-equilibrium conditions and the modeling of complexity 275 6.2 Materials science 279 6.3 Threshold phenomena in cellular dynamics 223 6.4 Modeling climatic change and variability 226 6.5 Probabilistic behavior and adaptive strategies in social insects 232 6.6 Self organization in human systems 238 Appendix 1 LINEAR STABILITY ANALYSIS 243 A 1.1 Basic equations 243 Al.2 The principle of linearized stability 247 Al.3 The characteristic equation 248 Al.4 Illustrations 257 Al.5 Systems exhibiting chaotic dynamics 254 Appendix2 BIFURCATION ANALYSIS 257 A2.I General properties 257 A2.2 Expansion of the solution in perturbation series 260 A2.3 The bifurcation equations 262 Appendix 3 PERTURBATION OF RESONANT MOTIONS IN NONINTEGRABLE CONSERVATIVE SYSTEMS 265 A3.1 The twist map