Lecture: Dynamical Processes on Networks

Brief Summary

This course provides a (mathematical) introduction to such network dynamical systems. We discuss a selection of fundamental dynamical phenomena over interconnected network systems, e.g., consensus and disagreement in averaging systems, epidemic spreading dynamics, opinion formation models and synchronization in coupled oscillators and networked control systems.

Organization

Organizational Details

Lecturer: Michael Schaub
Contact: michael.schaub [at] rwth-aachen.de
Time commitment: The course consists formally of 3 classes of lectures per week and 2 exercise classes. However, the lectures will be held in a 4 hours per week schedule, over a shorter timspan. The precise dates will be announced in RWTH Moodle.
ECTS credits: 6
Study programs: Bachelor / Master
Language: English

Due to the Corona situation, the course will held online via Zoom. A link will be send to participants, so please register via RWTH Online.

Schedule and important dates

First lecture: April 15, 14:30
Lecture times: Tuesday, 16:30-18:00, and Thursday, 14:30-16:00 (dates will be announced via Moodle)
Exercises: Monday, 16:30-18:00

(last updated: Fri 19 March – later announcements to participants will supersede the above information)

Prerequisites

There are no formal prerequisites, apart from a certain scientific and mathematical maturity. Depending on your preparation, some topics will be more accessible than others. Ideally, you will have some familiarity with Graph Theory, Linear Algebra, Probability Theory, and Dynamical Systems, but in particular the latter is not a must. We will make use of python for certain homework exercises. A short introduction to pyhton will be given.

Lectures and seminars at RWTH that cover related topics include (not an exhaustive list): Kombinatorische Graphentheorie (Informatik 1), Theorie verteilter und paralleler Systeme (Informatik 1), Algorithmen für die Entdeckung von Communities in sozialen Netzwerken (Informatik 5), …

Course Details

Overview

Many real-world systems may be described as a network of dynamically interacting entities. We interact with each other in a social contact network, over which rumors as well as pathogens cam spread; electrical energy is delivered by the power grid; the Internet enables almost instantaneous world-wide interactions; our economies rest upon a complex network of inter-dependencies spanning the globe. Networks are ubiquitous in complex biological, social, engineering, and physical systems. Understanding the dynamics of these systems is essential if we are to redesign them, or guide/control them towards different behaviours. Networked control problems abound, including multi-user communication, distributed computation and sensing, swarming, flocking, and synchronization of coupled oscillators.

This course provides a (mathematical) introduction to such network dynamical systems. We discuss a selection of fundamental dynamical phenomena over interconnected network systems, e.g., consensus and disagreement in averaging systems, epidemic spreading dynamics, opinion formation models and synchronization in coupled oscillators and networked control systems.

Course Language

The course language is English

Exercises

There will be two kinds of exercises:

  • Weekly excercises (mostly pen and paper) to deepen your understanding about the material presented in the lecture. These exercises will not be graded.
  • In addition, there are two larger homework assignments that will be graded. Sufficient marks in these two homework assignments will be a prerequisite to participate in the exam.

Exam

There will be a written exam associated to the course. Sufficient marks in the homework assignments are necessary to participate in the Exam. More precise details about the exam will be announced via RWTH Moodle.

Material

The course will mostly follow the Book “Lectures on Network Systems” by Francesco Bullo.
The book is freely available online at http://motion.me.ucsb.edu/book-lns