Understanding Complex Systems

Theory, Models and Applications

By: Thilo Gross (Editor), Hiroki Sayama (Editor)

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Hardcover | 1 September 2009

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Adding one and one makes two, usually. But sometimes things add up to more than the sum of their parts. This observation, now frequently expressed in the maxim "more is different", is one of the characteristic features of complex systems and, in particular, complex networks. Along with their ubiquity in real world systems, the ability of networks to exhibit emergent dynamics, once they reach a certain size, has rendered them highly attractive targets for research. The resulting network hype has made the word "network" one of the most in uential buzzwords seen in almost every corner of science, from physics and biology to economy and social sciences. The theme of "more is different" appears in a different way in the present v- ume, from the viewpoint of what we call "adaptive networks." Adaptive networks uniquely combine dynamics on a network with dynamical adaptive changes of the underlying network topology, and thus they link classes of mechanisms that were previously studied in isolation. Here adding one and one certainly does not make two, but gives rise to a number of new phenomena, including highly robust se- organization of topology and dynamics and other remarkably rich dynamical beh- iors.

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From the reviews:

"The book contains an exhaustive overview of various examples of realistic adaptive networks, some theoretical arguments on their behaviour and some methodological tools that can be applied in various situations. It contains 14 contributions by influential authors in the field ... . the book contributors have a different disciplinary background gives to this book an interesting inter-disciplinary flavour that modellers in any field will appreciate." (Floriana Gargiulo, Journal of Artificial Societies and Social Simulation, Vol. 13 (1), 2010)

"The volume articulates this perspective and provides a collection of groundbreaking research papers that illustrate its potential. ... The chapters are independent contributions, each with its own bibliography ... . However, the way the chapters were selected and organized leads to an overall flow that is easy to follow, and renders the volume an important and accessible reference for researchers." (H. Van Dyke Parunak, ACM Computing Reviews, January, 2010)

"The volume would ... serve as a good introduction to, and overview of, research on adaptive networks for someone entering the field. ... contains fourteen invited contributions, plus an introductory chapter by the editors. ... Overall, Adaptive Networks is a solid collection that brings together diverse facets of an exciting and growing field with many opportunities for further research." (Nicholas Geard, Artificial Life, Vol. 16 (4), 2010)

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Paperback

Published: 14th March 2012

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Adaptive Networks	p. 1
Introduction	p. 1
The Interplay Between State and Topology	p. 2
Timescale Separation and Critical Phenomena	p. 3
Self-Organization of Non-trivial Network Topologies	p. 4
Adaptive Networks with Inseparable Timescales	p. 5
In this Book	p. 6
References	p. 8
Real-World Examples of Adaptive Networks
Social Group Dynamics in Networks	p. 11
Introduction	p. 11
Construction of the Networks	p. 13
Finding Communities	p. 15
The Clique Percolation Method	p. 15
Preferential Attachment at the Level of Communities	p. 16
The Static Communities	p. 20
Validating the Communities	p. 22
Evolving Communities	p. 24
Statistical Properties of the Community Dynamics	p. 27
Basic Statistics	p. 27
Stationary and Lifetime	p. 29
Predicting Community Break Up	p. 30
Merging of Communities	p. 32
Conclusion	p. 34
References	p. 35
Time-Dependent Complex Networks: Dynamic Centrality, Dynamic Motifs, and Cycles of Social Interactions	p. 39
Dynamic Centrality in Large-Scale Communication Networks	p. 39
Dynamic Centrality in Spatial Proximity Social Networks	p. 44
Dynamic Network Motifs and Cycles of Social Interaction	p. 46
Summary	p. 48
References	p. 49
Adaptive Biological Networks	p. 51
Introduction	p. 51
Network Development in Mycelial Fungi	p. 52
Predicted Transport Characteristics of the Mycelial Network	p. 54
Comparison Between Predicted Transport and Experimental Transport	p. 58
Oscillations and Pulsatile Transport	p. 58
Network Robustness	p. 61
Simple Networks in the Plasmodial Slime Mould Physarum Polycephalum	p. 61
Universal Features of Biological Networks?	p. 65
References	p. 67
Self-Organization of Adaptive Networks
Self-Organized Criticality and Adaptation in Discrete Dynamical Networks	p. 73
Introduction	p. 73
Dynamics of Random Boolean Networks and Random Threshold Networks	p. 77
Underlying Graph Structure	p. 77
Random Boolean Networks	p. 79
Random Threshold Networks	p. 79
Basic Dynamical Properties of RBNs and RTNs	p. 80
Network Self-Organization from Co-evolution of Dynamics and Topology	p. 83
Activity-Dependent Rewiring	p. 83
Adaptive Thresholds - Time Scale Separation Leads to Complex Topologies	p. 90
Extension to Random Boolean Networks	p. 93
Correlation-Based Rewiring in Neural Networks	p. 96
Summary and Outlook	p. 101
References	p. 103
Self-Organization and Complex Networks	p. 107
Introduction	p. 107
Scale Invariance and Self-Organization	p. 109
Geometric Fractals	p. 109
Self-Organized Criticality	p. 111
Complex Networks	p. 115
Network Properties	p. 115
Network Models	p. 116
A Self-Organized Network Model	p. 122
Motivation	p. 123
Definition	p. 124
Analytical Solution	p. 125
Particular Cases	p. 128
Conclusions	p. 132
References	p. 133
Self-Organization of Network Structure in Coupled-Map Systems	p. 137
Introduction	p. 137
Adaptive Network of Logistic-Map Units	p. 138
Model Formulation	p. 139
Unit Dynamics	p. 140
Connection Dynamics	p. 143
Network Structure	p. 145
Dynamic Networks in the Desynchronized Phase	p. 147
Adaptive Network of Bursting Units	p. 153
Model Formulation	p. 153
Unit Dynamics	p. 154
Connection Dynamics	p. 155
Mechanism of Structure Formation	p. 158
Formation of Hierarchical Network Structure Triggered by External Input	p. 158
Summary and Discussion	p. 160
References	p. 162
Dynamical Optimization and Synchronization in Adaptive Complex Networks	p. 165
Introduction	p. 165
Phase Synchronization in the Kuramoto Model	p. 167
Complete Synchronization and Enhanced Synchronizability in Adaptive Complex Networks	p. 175
Complete Synchronization in Adaptive Complex Networks	p. 175
Enhanced Synchronizability in Adaptive Complex Networks	p. 180
Conclusions	p. 186
References	p. 187
Contact Processes and Epidemiology on Adaptive Networks
Contact Processes and Moment Closure on Adaptive Networks	p. 191
Introduction	p. 191
Opinion Formation - Theme and Variations	p. 193
Continuous Opinions	p. 194
Two-Valued Choice and Irreversible Discord	p. 195
The Influence of Bounded Tolerance	p. 197
Asymmetric Insertion of Influence	p. 199
Other Approaches	p. 201
Epidemic Spreading and Moment Closure	p. 201
The Adaptive SIS Model	p. 202
Other Approaches	p. 206
Summary and Outlook	p. 207
References	p. 208
Noise Induced Dynamics in Adaptive Networks with Applications to Epidemiology	p. 209
Introduction	p. 209
Model	p. 212
Bifurcation Structure	p. 214
Effect of Recovered Class on Fluctuations	p. 216
Delayed Outbreaks	p. 221
Lifetime of the Endemic Steady State	p. 222
Network Geometry	p. 223
Conclusions and Discussion	p. 225
References	p. 226
Social Games on Adaptive Networks
A Dynamic Model of Social Network Formation	p. 231
Introduction	p. 231
Making Friends: A Baseline Model of Uniform Reinforcement	p. 234
Friends I: Asymmetric Weights	p. 234
Friends II: Symmetrized Reinforcement	p. 235
Analysis of Friends I and II	p. 235
Making Enemies	p. 237
The Transfer Model	p. 238
The Resistance Model	p. 239
A Better Model?	p. 240
Perturbations of the Models	p. 240
Discounting the Past	p. 240
Analysis of Discounting the Past	p. 241
Introduction of Noise	p. 242
Noise and Discounting	p. 243
Reinforcement by Games of Nontrivial Strategy	p. 244
Rousseau's Stag Hunt	p. 244
Co-evolution of Structure and Strategy	p. 246
Conclusion	p. 247
References	p. 251
Evolutionary Games in Self-Organizing Populations	p. 253
Evolutionary Game Dynamics	p. 253
Active Linking	p. 254
Linking Dynamics	p. 255
Strategy Dynamics	p. 256
Separation of Timescales	p. 258
Effects of Active Linking	p. 260
Individual Based Linking Dynamics	p. 261
Specification of the Linking Dynamics	p. 261
Numerical Results	p. 263
Graph Structures Under Individual Based Linking Dynamics	p. 264
Discussion	p. 265
References	p. 266
The Diplomat's Dilemma: Maximal Power for Minimal Effort in Social Networks	p. 269
Introduction	p. 269
Definition of the Model	p. 271
Preliminaries	p. 271
Moves	p. 272
Strategies	p. 272
Strategy Updates and Stochastic Rewiring	p. 274
The Entire Algorithm	p. 274
Numerical Results	p. 275
Time Evolution	p. 275
Example Networks	p. 275
Effects of Strategies on the Network Topology	p. 277
Transition Probabilities	p. 282
Dependence on System Size and Noise	p. 283
Discussion	p. 284
References	p. 287
Part V
Graph-Rewriting Automata as a Natural Extension of Cellular Automata	p. 291
Introduction	p. 291
Formulation	p. 292
Rules of Graph-Rewriting Automata	p. 293
Update Procedure	p. 294
Simulation of Graph-Rewriting Automata	p. 295
Examples	p. 296
Rule Design by Hand-Coding	p. 297
Design of Self-replicating Turing Machine	p. 298
Rule Search by Evolutionary Computation	p. 300
Evolutionary Computation	p. 300
Simulation Results	p. 302
Exhaustive Trial	p. 303
Rule Representation	p. 304
Results	p. 304
Conclusions	p. 307
References	p. 308
Generative Network Automata: A Generalized Framework for Modeling Adaptive Network Dynamics Using Graph Rewritings	p. 311
Introduction	p. 311
About Graph Rewriting	p. 313
Definition of GNA	p. 314
Generality of GNA	p. 317
Computational Exploration of Possible Dynamics of Simple Binary-State GNA	p. 317
Assumptions	p. 317
Methods	p. 320
Results	p. 321
Conclusion	p. 329
References	p. 330
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Understanding Complex Systems

Theory, Models and Applications

At a Glance

Hardcover

Industry Reviews

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