Reviews of Nonlinear Dynamics and Complexity

✍ Scribed by Heinz Georg Schuster

• Publisher: Wiley-VCH
• Year: 2009
• Tongue: English
• Leaves: 260
• Series: Annual Reviews of Nonlinear Dynamics and Complexity VCH
• Category: Library

✦ Synopsis

Adopting a cross-disciplinary approach, the review character of this monograph sets it apart from specialized journals. The editor is advised by a first-class board of international scientists, such that the carefully selected and invited contributions represent the latest and most relevant findings. The resulting review uses a common language and enables both researchers and newcomers in both natural and social science as well as engineering to access the most important results.

✦ Table of Contents

Reviews of Nonlinear Dynamics and Complexity......Page 5
Contents......Page 7
Preface......Page 11
List of Contributors......Page 13
1.1 Introduction and Motivation......Page 15
1.2.1 Preliminary Considerations......Page 17
1.2.2 The Lack of Scale in Human Mobility......Page 19
1.3 Statistical Properties and Scaling Laws in Multi-Scale Mobility Networks......Page 22
1.3.1 Scaling Laws in the Topological Features of Multi-Scale Transportation Networks......Page 24
1.4 Spatially Extended Epidemic Models......Page 26
1.4.1 Disease Dynamics in a Single Population......Page 27
1.4.1.1 The SIS Model......Page 28
1.5 Spatial Models......Page 29
1.5.1 Continuity Limit and Fractional Transport......Page 32
1.5.2 Limiting Cases......Page 34
References......Page 37
2.1 Game Theory and Evolution......Page 39
2.2 The Replicator Dynamics......Page 40
2.3.1 Stochastic Evolutionary Game Dynamics......Page 43
2.3.2 Fixation Probabilities......Page 45
2.3.3.1 Unconditional Fixation Time......Page 48
2.3.3.2 Conditional Fixation Times......Page 50
2.3.4 The Moran Process and Weak Selection......Page 51
2.3.5 The Fermi Process......Page 55
2.4 From Finite to Infinite Populations (and Back Again)......Page 57
2.5 Applications......Page 60
2.5.1 The Prisoner’s Dilemma......Page 61
2.5.2 Rock-Paper-Scissors......Page 63
2.5.3 Voluntary Public Goods Games......Page 65
2.5.4 Punishment......Page 68
2.6 Concluding Remarks......Page 70
References......Page 71
3.1 Introduction......Page 77
3.2.1 Basic Definitions of Graph Theory......Page 80
3.2.2 Dynamic and Evolving Networks......Page 82
3.2.3 Adaptive Networks......Page 84
3.3 Ubiquity of Adaptive Networks Across Disciplines......Page 86
3.4 Robust Self-Organization Toward Criticality in Boolean Networks......Page 90
3.5.1 Leadership and the Division of Labor......Page 93
3.5.2 Self-Organization Towards Synchronizability......Page 96
3.6.1 Elevated Levels of Cooperation......Page 98
3.6.2 Struggle for Topological Position......Page 101
3.7.1 Epidemiological Models......Page 102
3.7.2 Opinion Formation......Page 111
3.8 Summary, Synthesis and Outlook......Page 112
3.8.1 The Four Hallmarks of Adaptive Networks......Page 113
3.8.2 Adaptive Networks: Future Impacts......Page 114
3.8.3 Towards a Unifying Theory of Adaptive Networks......Page 115
3.8.4 Future Challenges......Page 117
References......Page 118
4.1.1 Earthquake Statistics......Page 121
4.1.2 Modeling Earthquake Dynamics......Page 122
4.1.3.1 Fractal Geometry of Fault Surfaces......Page 124
4.1.3.2 Frequency–Size Distribution of Faults......Page 125
4.2.1 The Model......Page 129
4.2.2 Analysis of the Time Series......Page 131
4.2.3 The Gutenberg–Richter Law......Page 133
4.2.4 The Omori Law......Page 135
4.2.5 Temporal Distribution of Magnitudes of an Aftershock Sequence......Page 137
4.3.1 The Gutenberg–Richter Law......Page 139
4.3.3 The Temporal Distribution of Aftershock Magnitudes......Page 141
4.4 Fiber Bundle Model of Earthquakes......Page 151
4.5 Summary and Discussion......Page 153
C.1 Random Cantor Sets......Page 162
C.2 Regular Sierpinski Gaskets......Page 163
C.4 Percolating Clusters in a Square Lattice......Page 166
References......Page 169
5.1 Introduction......Page 173
5.2 Computational Models in Epilepsy Research......Page 179
5.2.1 From Microscopic to Macroscopic Modeling Approaches......Page 180
5.2.2 Modeling Epileptic Phenomena......Page 182
5.3 Measuring Interactions in Epileptic Networks......Page 185
5.3.1 Bivariate Time Series Analysis......Page 187
5.3.2 Multivariate Time-Series Analysis......Page 193
5.4 Conclusion......Page 197
References......Page 198
6.1 Introduction......Page 215
6.2.1 Clustering......Page 217
6.2.2 Dimensionality Reduction......Page 222
6.3 A New Quality Function for Structure Recognition in Networks......Page 224
6.3.1 The Optimal Image Graph......Page 227
6.3.2 Choice of a Penalty Function and Null Model......Page 228
6.3.3 Benchmark......Page 230
6.4 Clusters, Modularity and Graph Partitioning......Page 231
6.5 Modularity of Random Networks: Replica Method......Page 232
6.6 Modularity of Random Networks: Cavity Method......Page 236
6.7 Conclusion......Page 248
References......Page 250
Index......Page 253