Dynamical Processes on Networks
Lecture
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 can 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 an introduction to such network dynamical systems. We discuss a selection of fundamental dynamical phenomena over interconnected network systems, such as consensus and disagreement in averaging systems, epidemic spreading dynamics, opinion formation models and synchronization in coupled oscillators and networked control systems.
Homework and Exam
Exercises
There will be two kinds of exercises:
- Weekly excercises 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 RWTHmoodle.
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:
- Kombinatorische Graphentheorie - Informatik 1,
- Theorie verteilter und paralleler Systeme - Informatik 1,
- Algorithmen für die Entdeckung von Communities in sozialen Netzwerken - Informatik 5