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NetworksAn Introduction$
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Mark Newman

Print publication date: 2010

Print ISBN-13: 9780199206650

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199206650.001.0001

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Dynamical systems on networks

Dynamical systems on networks

A discussion of dynamical systems on networks, a subject area that is in its infancy but about which we nonetheless have some interesting results

Chapter:
(p.676) Chapter 18 Dynamical systems on networks
Source:
Networks
Author(s):

M. E. J. Newman

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199206650.003.0018

Many real-world processes — or simplified models of real-world processes — can be represented as dynamical systems on networks. The spread of news or information between friends, the movement of money through an economy, the flow of traffic on roads, data over the Internet, or electricity over the grid, the evolution of populations in an ecosystem, the changing concentrations of metabolites in a cell, and many other systems of scientific interest are best thought of as dynamical processes of one kind or another taking place on an appropriate network. In other, non-network contexts, the theory of dynamical systems is a well-developed branch of mathematics and physics. This chapter delves into some of this theory and shows how it can be applied to dynamical systems on networks. It focuses on deterministic systems of continuous real-valued variables evolving in continuous time t. Exercises are provided at the end of the chapter.

Keywords:   dynamical systems, dynamics on networks, deterministic systems, metabolites, dynamical processes

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