University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 10

Semester: 2

Availability restrictions: Not automatically available to General Degree students

Planned timetable: 10.00 am Mon (even weeks), Tue and Thu

This module aims to introduce students to the basic ideas of the modern theory of dynamical systems and to the concepts of chaos and strange attractors. The module will include: period doubling; intermittency and chaos; geometrical approach to differential equations; homoclinic and heteroclinic orbits; Poincaré sections; the Smale horseshoe mapping; centre manifold theory.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass MT3504

Learning and teaching methods and delivery

Weekly contact: 2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).

Scheduled learning hours: 35

Guided independent study hours: 115

Assessment pattern

As used by St Andrews: 2-hour written examination = 85%; Project = 15%


Re-assessment: Oral examination = 100%

Personnel

Module coordinator: Professor T Neukirch
Module teaching staff:
Module coordinator email tn3@st-andrews.ac.uk

Intended learning outcomes

• Understand the basic properties and evolution of discrete and continuous time dynamical systems
• Be able to understand the key building blocks and aspects of chaos and chaotic behaviour in dynamic systems
• Apply knowledge from mathematical methods (e.g. ODEs, Jacobian matrix, calculating eigenvalues and eigenvectors) to gain iquantitaive and qualitative understanding about the stability/instability of a dynamical system and how this is related to chaotic behaviour
• Understand the nature of the fundamental elements of dynamics in systems, such as: maps, bifurcations, attractors, cascades, horseshoes, basins, homoclinic orbits, Lyapunov exponents and functions