Dynamical System and Chaos

5 credits

Syllabus, Master's level, 1FA152

A revised version of the syllabus is available.
Education cycle
Second cycle
Main field(s) of study and in-depth level
Mathematics A1N, Physics A1N
Grading system
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 10 February 2020
Responsible department
Department of Physics and Astronomy

Entry requirements

120 credits with Mechanics III (analytical mechanics). Computer Programming I.

Learning outcomes

On completion of the course, the student should be able to:

  • analyse and characterize dynamical systems classifying its fixed points, stability and possibly bifurcations and limit cycles in one and more dimensions,
  • apply the knowledge gained in the course to generate the phase space in one and more dimensions,
  • describe and critically assess the characteristics of Lorenz equations and one dimensional maps,
  • identify and contrast chaotic and non chaotic regimes of dynamical systems,
  • relate the theory learned during the course to experimental observations carried out during the laboratory activity and to explain the underlying physical aspect governing the dynamics of the system,
  • discuss and summarize the laboratory observations in a report.


Flows on the line, bifurcations in one dimension, linear systems, phase plane, limit cycles, bifurcations in two and higher dimensions, Lorenz equations, one dimensional maps, fractals and strange attractors.

Examples from biology, meteorology, fluid dynamics and finance.

Laboratory experiments concerning chaotic behaviors of dynamical systems.


Lectures, lessons and laboratory experiments. The course makes use of subject integrated communication training with feedback and self evaluation.


Written examination at the end of the course (3 credit). Hand-in exercises (1 credit). Laboratory experiments with written reports (1 hp).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.