Complexity and Networks (University of Groningen)

Overview

This is a required course for University of Groningen students in the programs MSc Mathematics and MSc Applied Mathematics. I co-taught this course from 2017 to 2019.

Course Description

The course gives an overview of topics on Complexity and Networks. In the first part, consisting of four lectures, we discuss synchronization and the stability of synchronized solutions for systems connected in a network. The topics are:

• Mean field approach to the Kuramoto model
• Linear stability of the incoherent state in the Kuramoto model
• Ott-Antonsen ansatz in the Kuramoto model
• Graph Laplacian
• Diffusion process in a network
• Master stability function
• Analysis of a model for circadian rhythms

More information about the course, including the other 3 parts, is available on Ocasys.

Lectures

The slides for the 4 lectures are available through the following links. The slides are made available under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA-3.0).

• The Kuramoto model - Part I
• The Kuramoto model - Part II
• Graph Laplacian and Master Stability Function
• Circadian rhythms

The slides have been converted from Markdown to Reveal.js using Pandoc. MathJax takes care of typesetting the mathematics. The slides should display properly in any modern browser.