Dynamical Systems on Networks: A Tutorial

ISBN-13: 9783319266404 / Angielski / Miękka / 2016 / 80 str.

Mason A. Porter; James P. Gleeson

Opis

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.

Recenzje

"This book by Porter and Gleeson is an excellent tutorial of dynamical systems interconnected as networks. ... the book under review is highly recommended for students and researchers new to the dynamical systems view of networks. The authors take the best possible approach to presenting a problem for a very large audience." (Juan Gonzalo Bajaras-Ram rez, Mathematical Reviews, February, 2017)

"The book is a relatively concise tutorial and a summary of references for the study of dynamical systems on networks. ... This tutorial may serve as an accompanying source for the introduction to the field 'Dynamical systems on networks'." (Serhiy Yanchuk, zbMATH 1369.34001, 2017)

Spis treści

Introduction: How Does Nontrivial Network Connectivity Affect Dynamical Processes on Networks.- A Few Basic Concepts.- Examples of Dynamical Systems.- General Considerations.- Software Implementation.- Dynamical Systems on Dynamical Networks.- Other Resources.- Conclusion, Outlook, and Open Problems.- Appendix.