Modeling of Complex Systems

PrefaceAcknowledgmentsSuggestions for Term Projects1 An Approach to the Problem Introduction 1 What Are Large-Scale Systems? 2 How to Handle Complex Systems 3 Issues at Large Exercises Suggestions for Further Reading2 Language of System Theory Introduction 1 Goals, Objectives, and Indicators 2 Attributes and Resolution Levels 3 Systems Measurement 4 The Taxonomy of System Concepts Exercises Suggestions for Further Reading3 The Modeling Process Introduction 1 Taxonomy of Model Types 2 Steps in Model Building 3 Simulation 4 Algorithms and Heuristics 5 Simulation Languages Exercises Suggestions for Further Reading4 Primitive Models Introduction 1 Establishing Relations Using Physical Laws 2 Establishing Relations via Curve Fitting 3 More Complex Parameter Estimation Problems 4 Elementary State Transition Models Exercises Suggestions for Further Reading5 Forecasting Introduction 141 1 The Nature of Data 2 Statistical Attributes of Data 3 Probability Distributions and Their Underlying Mechanisms 4 Generation of Random Numbers 5 Time Series 6 A Model for Generating River Flow Data Exercises Suggestions for Further Reading6 Recognition off Patterns Introduction 1 Fundamental Problems of Recognition 2 Neighborhoods and Distances 3 A Hierarchical Approach to Clustering 4 Nonhierarchical Approaches to Clustering 5 Individual and Group Preference Patterns Exercises Suggestions for Further Reading7 Static Equilibrium Models Introduction 1 Graphical Models and Matrix Models 2 Patterns of Group Structure 3 Input-Output Type Models 4 Decomposition of Large Systems 5 Routing Problems Exercises Suggestions for Further Reading8 Analysis of Competitive Situations Introduction 1 Elementary Ideas About Optimization 2 Optimization with Equality Constraints 3 Problems with Inequality Constraints 4 The Linear Programming Model 5 The Simplex Algorithm 6 Duality in Linear Programming Models 7 Dynamic Planning with Linear Programming Exercises Suggestions for Further Reading9 Linear Dynamical Structure Introduction 1 Pictorial Representation of System Structure 2 Transfer Function Models 3 The Behavior of Systems: Stability 4 State Space Models 5 System Control 6 Optimum Control of River Pollution Exercises Suggestions for Further Reading10 Growth and Decay Processes Introduction 1 Discrete Growth Processes 2 Continuous Growth 3 Limits to Growth 4 Competition among Species 5 Growth Processes and Integral Equations 6 The Discrete Event Approach 7 Population Planning Exercises Suggestions for Further ReadingAppendix 1 Sets and Relations Sets and Algebra of Sets Relations Mapping and FunctionsAppendix 2 Elements of Probability Introduction Random Experiments and Sample Spaces Probability Random Variables and Probability DistributionsAppendix 3 Elements of Matrix Methods Introduction Matrix Addition and Multiplication Algebra with Binary Matrices Other Useful Definitions Inversion of a Matrix Eigenvalues and EigenvectorsAppendix 4 Differential Equations Introduction What Are Differential Equations?Index