# 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

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .