Mathematics

Dynamical Systems

Module code: G5126
Level 6
15 credits in spring semester
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination

You will discuss concepts such as stability, attractor, basin of attraction and chaos for general dynamical systems, and then study them for dynamical systems given by ordinary differential equations and iterations of maps in particular.

The module uses methods from analysis, but also many sketches to visually understand the concepts.

Module learning outcomes

• Understand the general concepts of dynamical systems and be able to give examples of dynamical systems.
• Perform a stability analysis of fixed points and periodic orbits in ordinary differential equations using linearization and Lyapunov functions.
• Describe and apply linearization around fixed points of discrete dynamical systems.
• Prove existence results on attractors and properties of omega limit sets for general dynamical systems.