Syllabus for Dynamical System and Chaos

Dynamiska system och kaos


  • 5 credits
  • Course code: 1FA152
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Physics A1N, Mathematics A1N
  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2010-03-18
  • Established by:
  • Revised: 2021-03-26
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: Autumn 2022
  • Entry requirements:

    120 credits with Mechanics III (analytical mechanics). Computer Programming I. Proficiency in English equivalent to the Swedish upper secondary course English 6.

  • Responsible department: Department of Physics and Astronomy

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.

Reading list

Reading list

Applies from: Autumn 2022

Some titles may be available electronically through the University library.

  • Strogatz, Steven H. Nonlinear dynamics and chaos : with applications to physics, biology, chemistry and engineering

    Reading, Mass.: Addison-Wesley, 1994

    Find in the library


Last modified: 2022-04-26