Dynamical Systems on Networks: A Tutorial

TL;DR

This tutorial introduces the study of dynamical systems on networks, emphasizing analytically tractable cases, key examples, theoretical insights, and future directions in the field.

Contribution

It provides a comprehensive overview of simple dynamical systems on networks, including theoretical results, software tools, and extensions to dynamic networks.

Findings

Analytical tractability of simple network dynamical systems

Key examples illustrating system behaviors

Overview of software implementations and future outlook

Abstract

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.