Dynamical Systems on Networks: A Tutorial

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Springer, Mar 31, 2016 - Mathematics - 80 pages

This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios.

This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks.

Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow

of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics, and co-Director of MACSI, at the University of Limerick, Ireland.

 

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Contents

How Does Nontrivial Network Connectivity Affect Dynamical Processes on Networks?
1
2 A Few Basic Concepts
3
3 Examples of Dynamical Systems
5
4 General Considerations
29
5 Software Implementation
46
6 Dynamical Systems on Dynamical Networks
49
7 Other Resources
53
8 Conclusion Outlook and Open Problems
55
HighAccuracy Approximation Methods for General BinaryState Dynamics
57
References
66
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