Syllabus for Dynamical System and Chaos

Dynamiska system och kaos

Syllabus

  • 5 credits
  • Course code: 1FA152
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Physics A1N, Mathematics A1N

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle
    G1N: has only upper-secondary level entry requirements
    G1F: has less than 60 credits in first-cycle course/s as entry requirements
    G1E: contains specially designed degree project for Higher Education Diploma
    G2F: has at least 60 credits in first-cycle course/s as entry requirements
    G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    GXX: in-depth level of the course cannot be classified.

    Second cycle
    A1N: has only first-cycle course/s as entry requirements
    A1F: has second-cycle course/s as entry requirements
    A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    AXX: in-depth level of the course cannot be classified.

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2010-03-18
  • Established by:
  • Revised: 2020-02-10
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 30, 2020
  • Entry requirements: 120 credits with Mechanics III (analytical mechanics). Computer programming I.
  • Responsible department: Department of Physics and Astronomy

Learning outcomes

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

  • analyze 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.

Content


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. 

Instruction

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

Assessment

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: week 30, 2020

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

    Reading, Mass.: Addison-Wesley, 1994

    Find in the library

    Mandatory