Preface of the First Edition Preface of the Second Edition Notations 1 Introduction 1.1 What is a Complex System？ 1.2 What is a Model？ 1.3 What is a Dynamical System？ Exercises Solutions Summary 2 How to Build Up a Model 2.1 Lotka—Volterra Model 2.2 More R，ealistic Predator—Prey Models 2.3 A Model with a Stable Limit Cycle 2.4 Fluctuating Environments 2.5 Hutchinson's Time—Delay Model 2.6 Discrete—Time Models 2.7 Lattice Models Exercises Solutions Summary 3 Differential Equations 3.1 Flows 3.2 Linearization and Stability 3.2.1 Linear Systems 3.2.2 Nonlinear Systems 3.3 Graphical Study of Two—Dimensional Systems 3.4 Structural Stability 3.5 Local Bifurcations of Vector Fields 3.5.1 One—Dimensional Vector Fields 3.5.2 Equivalent Families of Vector Fields 3.5.3 Hopf Bifurcation 3.5.4 Catastrophes 3.6 Influence of Diffusion 3.6.1 Random Walk and Diffusion 3.6.2 One—Population Dynamics with Dispersal 3.6.3 Critical Patch Size 3.6.4 Diffusion—Induced Instability Exercises Solutions Summary 4 Recurrence Equations 4.1 Iteration of Maps 4.2 Stability 4.3 Poincare Maps 4.4 Local Bifurcations of Maps 4.4.1 Maps on R 4.4.2 The Hopf Bifurcation 4.5 Sequences of Period—Doubling Bifurcations 4.5.1 Logistic Model
4.5.2 Universality Exercises Solutions Summary 5 Chaos 5.1 Defining Chaos 5.1.1 Dynanucs of the Logistic Map f4 5.1.2 Definition of Chaos 5.2 Routes to Chaos 5.3 Characterizing Chaos 5.3.1 Stochastic Properties 5.3.2 Lyapunov Exponent 5.3.3 "Period Threelmplies Chaos" 5.3.4 Strange Attractors 5.4 Chaotic Discrete—Time Models 5.4.1 One—Population Models 5.4.2 The Henon Map 5.5 Chaotic Continuous—Time Models 5.5.1 The Lorenz Model Exercises Solutions Summary 6 Spatial Models 6.1 Cellular Automata 6.2 Number—Conserving Cellular Automata 6.3 Eventually Number—Conserving Cellular Automata 6.4 Approximate Methods 6.5 Generalized Cellular Automata 6.6 Kinetic Growth Phenomena 6.7 Site—Exchange Cellular Automata 6.8 Agent—Based Spatial Models 6.9 Sociophysics Exercises Solutions Summary 7 Networks 7.1 The Small—World Phenomenon 7.2 Graphs 7.3 Random Networks 7.4 Small—World Networks 7.4.1 Watts—Strogatz Model 7.4.2 Newman—Watts Model 7.4.3 Highly Connected Extra Vertex Model 7.5 Scale—Free Networks 7.5.1 Empirical Results 7.5.2 A Few Models Exercises Solutions Summary 8 Power—Law Distributions
8.1 Classical Examples 8.2 A Few Notions of Probability Theory 8.2.1 Basic Definitions 8.2.2 Central Limit Theorem 8.2.3 Lognormal Distribution 8.2.4 Levy Distributions 8.2.5 Truncated Levy Distributions 8.2.6 Student's t—Distribution 8.2.7 A Word About Statistics 8.3 Empirical Results and Tentative Models 8.3.1 Financial Markets 8.3.2 Demographic and Area Distribution 8.3.3 Family Names 8.3.4 Distribution of Votes 8.4 Self—Organized Criticality 8.4.1 The Sandpile Model 8.4.2 Drossel—Schwabl Forest Fire Model 8.4.3 Punctuated Equilibria and Darwinian Evolution 8.4.4 Real— Life Phenomena Exercises Solutions Summary Glossary References Index
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