Introduction to the Modeling and Analysis of Complex Systems

ContentsI Preliminaries 11 Introduction 31.1 Complex Systems in a Nutshell . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Topical Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Fundamentals of Modeling 112.1 Models in Science and Engineering . . . . . . . . . . . . . . . . . . . . . . 112.2 How to Create a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Modeling Complex Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 What Are Good Models? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5 A Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22II Systems with a Small Number of Variables 273 Basics of Dynamical Systems 293.1 What Are Dynamical Systems? . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Phase Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3 What Can We Learn? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 Discrete-Time Models I: Modeling 354.1 Discrete-Time Models with Difference Equations . . . . . . . . . . . . . . . 354.2 Classifications of Model Equations . . . . . . . . . . . . . . . . . . . . . . . 364.3 Simulating Discrete-Time Models with One Variable . . . . . . . . . . . . . 394.4 Simulating Discrete-Time Models with Multiple Variables . . . . . . . . . . . 464.5 Building Your Own Model Equation . . . . . . . . . . . . . . . . . . . . . . . 514.6 Building Your Own Model Equations with Multiple Variables . . . . . . . . . 55xv