Mathematics

Dynamical Systems

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

General dynamical systems:

  • semiflow
  • stability and attraction
  • omega-limit set
  • global attractor.

Ordinary Differential Equations:

  • linear systems
  • Lyapunov function
  • linearised systems around fixed points
  • two-dimensional systems
  • periodic orbit.

Discrete systems (iterations):

  • linear systems
  • linearised systems around fixed points
  • chaos.

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.