# Dynamical Systems on Networks: A Tutorial

arXiv: https://arxiv.org/abs/1403.7663 · HTML: https://mlsanity.com/paper/1403.7663/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2014.

## Built on by (most cited first, 7 of 7)

- [CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2306.11216/) (2023)
- [A Dynamical Systems Perspective on the Analysis of Neural Networks](https://mlsanity.com/paper/2507.05164/) (2025)
- [Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach](https://mlsanity.com/paper/2208.04405/) (2022)
- [Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy](https://mlsanity.com/paper/2605.30432/) (2026)
- [Topological data analysis of truncated contagion maps](https://mlsanity.com/paper/2203.01720/) (2022)
- [Monte Carlo Physarum Machine: Characteristics of Pattern Formation in Continuous Stochastic Transport Networks](https://mlsanity.com/paper/2204.01256/) (2022)
- [Matrix-weighted networks for modeling multidimensional dynamics](https://mlsanity.com/paper/2410.05188/) (2024)

## Abstract (arXiv)

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.