Table of Contents
Preface ix
1 Introduction 1
1.1 What Is a Complex System? 9
1.2 A Brief History of Complexity Science 11
1.2.1 Cybernetics and Systems Theory 12
1.2.2 Dynamical Systems Theory 13
1.2.3 Cellular Automata 15
1.2.4 The Rise of Complexity Science 16
2 Examples of Complex Systems 19
2.1 Matter and Radiation 19
2.2 The Universe 29
2.3 The Climate System 33
2.4 Eusocial Insects 37
2.4.1 Ant Colonies 38
2.4.2 Honeybee Hives 41
2.5 Markets and Economies 45
2.6 The World Wide Web 54
2.7 The Human Brain 57
3 Features of Complex Systems 63
3.1 Numerosity 66
3.2 Disorder and Diversity 68
3.3 Feedback 70
3.4 Non-Equilibrium 71
3.5 Interlude: Emergence 73
3.6 Order and Self-Organisation 76
3.7 Nonlinearity 77
3.8 Robustness 79
3.9 Nested Structure and Modularity 81
3.10 History and Memory 81
3.11 Adaptive Behaviour 82
3.12 Different Views of Complexity 84
4 Measuring Features of Complex Systems 87
4.1 Numerosity 88
4.2 Disorder and Diversity 89
4.3 Feedback 93
4.4 Non-Equilibrium 95
4.5 Spontaneous Order and Self-Organisation 96
4.6 Nonlinearity 99
4.6.1 Nonlinearity as Power Laws 99
4.6.2 Nonlinearity versus Chaos 100
4.6.3 Nonlinearity as Correlations or Feedback 101
4.7 Robustness 101
4.7.1 Stability Analysis 102
4.7.2 Critical Slowing Down and Tipping Points 103
4.7.3 Self-Organised Criticality and Scale Invariance 105
4.7.4 Robustness of Complex Networks 106
4.8 Nested Structure and Modularity 107
4.9 History and Memory 110
4.10 Computational Measures 110
4.10.1 Thermodynamic Depth 111
4.10.2 Statistical Complexity and True Measure Complexity 111
4.10.3 Effective Complexity 114
4.10.4 Logical Depth 115
5 What Is a Complex System? 117
5.1 Nihilism about Complex Systems 117
5.2 Pragmatism about Complex Systems 119
5.3 Realism about Complex Systems 120
5.3.1 Generic Conceptions of Complexity 121
5.3.2 Physical Conceptions of Complexity 122
5.3.3 Computational Conceptions of Complexity 124
5.3.4 Functional Conceptions of Complexity 124
5.4 The Varieties of Complex Systems 126
5.5 Implications 132
Appendix - Some Mathematical Background 135
A Probability Theory 135
B Shannon Information Theory 137
C Algorithmic Information Theory 139
D Complex Networks 140
Bibliography 143
Index 163
