Exploring complexity : an introduction / Grégoier Nicolis, Iya Prigogine.

Format:

Book

Author/Creator:

Nicolis, G., 1939-

Contributor:

Prigogine, I. (Ilya)

Language:

English

Subjects (All):

Science--Philosophy.

Science.

Complexity (Philosophy).

Physical Description:

xi, 313 pages : illustrations ; 24 cm

Place of Publication:

New York : W.H. Freeman, [1989]

Summary:

Unexpected discoveries in nonequilibrium physics and nonlinear dynamics are changing our understanding of complex phenomene. Recent research has revealed fundamental new properties of matter in far-from-equilibrium conditions, and the prevalence of instability -- where small changes in initial conditions may lead to amplified effects.

Contents:

Prologue: Science in an Age of Transition 1

1 Complexity In Nature 5

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

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 93

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 115

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 160

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 [Lambda] 205

5.8 Gibbs ensembles and Boltzmann ensembles 209

5.9 Kinetic theory 210

5.10 Resonance and light-matter interaction 212

6 Complexity And The Transfer Of Knowledge 217

6.1 Nonlinear dynamics in far-from-equilibrium conditions and the modeling of complexity 218

6.2 Materials science 219

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

A1.1 Basic equations 243

A1.2 The principle of linearized stability 247

A1.3 The characteristic equation 248

A1.5 Systems exhibiting chaotic dynamics 254

Appendix 2 Bifurcation Analysis 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 265

A3.2 Effect of the perturbation in the case of rational rotation numbers 268

A3.3 Homoclinic points 270

Appendix 4 Reconstruction Of The Dynamics Of Complex Systems From Time Series Data. Application To Climatic Variability 275

A4.2 Theoretical background for data analysis 278

A4.3 The climatic attractor 279

A4.4 Conclusion and perspectives 281

Appendix 5 Primordial Irreversible Processes 283

A5.2 Standard cosmological model 285

A5.3 Black holes 285

A5.4 The role of irreversibility 287.

Notes:

Includes bibliographical references and index.

ISBN:

0716718596

071671860X

OCLC:

18989681