REVIEWS OF NONLINEAR DYNAMICS AND COMPLEXITY

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.

Editor: Heinz Georg Schuster
Editorial Board:
Christoph Adami, California Institute of Technology, USA
Stefan Bornholdt, University of Bremen, Germany
Wolfram Just, Queen Mary University of London, UK
Kunihiko Kaneko, University of Tokyo, Japan
Ron Lifshitz, Tel Aviv University, Israel
Ernst Niebur, Johns Hopkins University, Baltimore, USA
Guenter Radons, TU Chemnitz, Germany
Eckehard Schoell, TU Berlin, Germany
Hong Zhao, Xiamen University, China


Heinz Georg Schuster is Professor (em.) of Theoretical Physics at the University of Kiel in Germany. In 1971 he attained his doctorate and in 1976 he was appointed Professor at the University of Frankfurt am Main in Germany. He was a visiting professor at the Weizmann-Institute of Science in Israel and at the California Institute of Technology in Pasadena, USA. He is author and editor of research monographs and topical handbooks on chaos theory, nonlinear dynamics and neural networks, but also on popular science books.

Preface.
List of Contributors.
1 Human Mobility and Spatial Disease Dynamics (Dirk Brockmann).
1.1 Introduction and Motivation.
1.2 Quantitative Assessments of Human Mobility.
1.3 Statistical Properties and Scaling Laws in Multi-ScaleMobility Networks.
1.4 Spatially Extended Epidemic Models.
1.5 Spatial Models.
2 Stochastic Evolutionary Game Dynamics (Arne Traulsen and Christoph Hauert).
2.1 Game Theory and Evolution.
2.2 The Replicator Dynamics.
2.3 Evolutionary Games in Finite Populations.
2.4 From Finite to Infinite Populations (and Back Again).
2.5 Applications.
2.5.1 The Prisoner’s Dilemma.
2.6 Concluding Remarks.
References.
3 Dynamic and Topological Interplay in Adaptive Networks (Bernd Blasius and Thilo Gross).
3.1 Introduction.
3.2 Adaptive Networks: A Definition.
3.3 Ubiquity of Adaptive Networks Across Disciplines.
3.4 Robust Self-Organization Toward Criticality in Boolean Networks.
3.5 Adaptive Connection Weights in Coupled Oscillator Networks.
3.6 Cooperation in Games on Adaptive Networks.
3.7 Dynamics and Phase Transitions in Opinion Formation and Epidemics.
3.8 Summary, Synthesis and Outlook.
References.
4 Fractal Models of Earthquake Dynamics (Pathikrit Bhattacharya, Bikas K. Chakrabarti, Kamal, and Debashis Samanta).
4.1 Introduction.
4.2 Two-Fractal Overlap Model.
4.3 Comparison with Observations.
4.4 Fiber Bundle Model of Earthquakes.
4.5 Summary and Discussion.
C.1 Random Cantor Sets.
C.2 Regular Sierpinski Gaskets.
C.3 Random Sierpinski Gaskets.
C.4 Percolating Clusters in a Square Lattice.
References.
5 Epilepsy (Klaus Lehnertz, Stephan Bialonski, Marie-Therese Horstmann, Dieter Krug, Alexander Rothkegel, Matthäus Staniek, and Tobias Wagner).
5.1 Introduction.
5.2 Computational Models in Epilepsy Research.
5.3 Measuring Interactions in Epileptic Networks.
5.4 Conclusion.
References.
6 Structure in Networks (Jörg Reichardt and Stefan Bornholdt).
6.1 Introduction.
6.2 Multivariate Data Versus Relational Data.
6.3 A New Quality Function for Structure Recognition in Networks.
6.4 Clusters, Modularity and Graph Partitioning.
6.5 Modularity of Random Networks: Replica Method.
6.6 Modularity of Random Networks: Cavity Method.
6.7 Conclusion.
References.
Index.