MT4508 Dynamical Systems

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

10.00 am Mon (weeks 2, 4, 6, 8, 11), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof C E Parnell

Prof C E Parnell
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Prof Clare Parnell

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

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-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT3504

Assessment pattern

2-hour written examination = 85%; Project = 15%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

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

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

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