Dynamical Systems on Networks: A Tutorial

✍ Scribed by Mason Porter, James Gleeson (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 91
• Series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials 4
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiv
Introduction: How Does Nontrivial Network Connectivity Affect Dynamical Processes on Networks?....Pages 1-2
A Few Basic Concepts....Pages 3-4
Examples of Dynamical Systems....Pages 5-27
General Considerations....Pages 29-45
Software Implementation....Pages 47-48
Dynamical Systems on Dynamical Networks....Pages 49-51
Other Resources....Pages 53-54
Conclusion, Outlook, and Open Problems....Pages 55-56
Back Matter....Pages 57-80

✦ Subjects

Dynamical Systems and Ergodic Theory; Complex Networks; Biological Networks, Systems Biology; Systems Biology