Dynamics of Complex Systems (Studies in Nonlinearity)

Description

The study of complex systems in a unified framework has become recognized in recent years as a new scientific discipline, the ultimate in the interdisciplinary fields. Breaking down the barriers between physics, chemistry, and biology and the so-called soft sciences of psychology, sociology, economics and anthropology, this text explores the universal physical and mathematical principles that govern the emergence of complex systems from simple components. Dynamics of Complex Systems is the first text describing the modern unified study of complex systems. It is designed for upper-undergraduate/beginning graduate level students, and covers a broad range of applications in a broad array of disciplines. A central goal of this text is to develop models and modeling techniques that are useful when applied to all complex systems. This is done by adopting both analytic tools, including statistical mechanics and stochastic dynamics, and computer simulation techniques, such as cellular automata and Monte Carlo. In four sets of paired, self-contained chapters, Yaneer Bar-Yam discusses complex systems in the context of neural networks, protein folding, living organisms, and finally, human civilization itself. He explores fundamental questions about the structure, dynamics, evolution, development and quantitative complexity that apply to all complex systems. In the first chapter, mathematical foundations such as iterative maps and chaos, probability theory and random walks, thermodynamics, information and computation theory, fractals and scaling, are reviewed to enable the text to be read by students and researchers with a variety of backgrounds. –This text refers to the Paperback edition.

Book Info

Describes the modern unified study of complex systems. Develops models and modeling techniques that are useful when applied to all complex systems. Discusses complex systems in the context of neural networks, protein folding, living organisms. DLC: Biomathematics.

Table of Contents

Preface
Acknowledgments
Overview: The Dynamics of Complex Systems - Examples, Questions, Methods and Concepts 1
1 Introduction and Preliminaries 16
1.1 Iterative Maps (and Chaos) 19
1.2 Stochastic Iterative Maps 38
1.3 Thermodynamics and Statistical Mechanics 58
1.4 Activated Processes (and Glasses) 95
1.5 Cellular Automata 112
1.6 Statistical Fields 145
1.7 Computer Simulations (Monte Carlo, Simulated Annealing) 186
1.8 Information 214
1.9 Computation 235
1.10 Fractals, Scaling and Renormalization 258
2 Neural Networks I: Subdivision and Hierarchy 295
2.1 Neural Networks: Brain and Mind 296
2.2 Attractor Networks 300
2.3 Feedforward Networks 322
2.4 Subdivided Neural Networks 328
2.5 Analysis and Simulations of Subdivided Networks 345
2.6 From Subdivision to Hierarchy 364
2.7 Subdivision as General Phenomenon 366
3 Neural Networks II: Models of Mind 371
3.1 Sleep and Subdivision Training 372
3.2 Brain Function and Models of Mind 393
4 Protein Folding I: Size Scaling of Time 420
4.1 The Protein-Folding Problem 421
4.2 Introduction to the Models 427
4.3 Parallel Processing in a Two-Spin Model 432
4.4 Homogeneous Systems 435
4.5 Inhomogeneous Systems 458
4.6 Conclusions 471
5 Protein Folding II: Kinetic Pathways 472
5.1 Phase Space Channels as Kinetic Pathways 473
5.2 Polymer Dynamics: Scaling Theory 477
5.3 Polymer Dynamics: Simulations 488
5.4 Polymer Collapse 503
6 Life I: Evolution - Origin of Complex Organisms 528
6.1 Living Organisms and Environments 529
6.2 Evolution Theory and Phenomenology 531
6.3 Genome, Phenome and Fitness 542
6.4 Exploration, Optimization and Population Interactions 550
6.5 Reproduction and Selection by Resources and Predators 576
6.6 Collective Evolution: Genes, Organisms and Populations 604
6.7 Conclusions 619
7 Life II: Developmental Biology - Complex by Design 621
7.1 Developmental Biology: Programming a Brick 621
7.2 Differentiation: Patterns in Animal Colors 626
7.3 Developmental Tool Kit 678
7.4 Theory, Mathematical Modeling and Biology 688
7.5 Principles of Self-Organization as Organization by Design 691
7.6 Pattern Formation and Evolution 695
8 Human Civilization I: Defining Complexity 699
8.1 Motivation 699
8.2 Complexity of Mathematical Models 705
8.3 Complexity of Physical Systems 716
8.4 Complexity Estimation 759
9 Human Civilization II: A Complex(ity) Transition 782
9.1 Introduction: Complex Systems and Social Policy 783
9.2 Inside a Complex System 788
9.3 Is Human Civilization a Complex System? 791
9.4 Toward a Networked Global Economy 796
9.5 Consequences of a Transition in Complexity 815
9.6 Civilization Itself 822
Additional Readings 827
Index 839

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