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Chaos and Nonlinear Physics 7.5 credits

Kaos och Ickelinjär Fysik
Second cycle, F7030T
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Education level
Second cycle
Grade scale
G U 3 4 5
Subject group (SCB)

Entry requirements

Physics 30hp and Linear Algebra.

More information about English language requirements


The selection is based on 20-285 credits

Course Aim
It is well known that all physical systems (except in quantum mechanics) are nonlinear. Former limitations to linear systems was of practical nature, as they generally were the only ones which could be exactly solved. By working with user-friendly computer software like Maple the knowledge gained can be applied to problems that would be impossible to study by "paper and pen alone".
To teach basic methods of nonlinear physics, which the student can use in his/her continued education, reserch of future work.

1. The world - a nonlinear system!
2. Introduction to Maple
3. Modelling Nature
4. Nonlinear systems I: Examples from a) Mechanics, b) Population dynamics, c) Electrical circuits, d) Chemical osillations, e) Heartbeats
5. Nonlinear systems II: a) Structure formation, b) Solitons, c) Chaos
6. Topological analysis: a) Singular points, b) Phase-plane analysis, c) Bifurcations
7. Limit-cycles: a) Stability, b) Mathematical theorems
8. Forced oscillations: a) Examples, b) Chaotic oscillations, c)"Strange attractors" d) Chaos in Hamiltonian system
9. Nonlinear mapping: a) Logistic mapping, b) Fix-points and stability, c) Period doubling towards chaos, d) The Lyapunov exponent, e) 2-and 3-dimensional mappings, f) Chaos control
10. Nonlinear partial differential equations: a) Examples, b) Nonlinear superposition, c)Solitary waves d) Numerical simultation, e) Inverse scattering method, f) Solitons

Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.

If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.
Hand-in assignments.

Johan Hansson

Transition terms
The course F7030T is equal to F7001T

Literature. Valid from Autumn 2010 Sp 1 (May change until 10 weeks before course start)
Nonlinear Physics With Maple for Scientists and Engineers, latest edition
R.H. Enns, G.C. McGuire. (Contains CD-ROM).

Course offered by
Department of Engineering Sciences and Mathematics

CodeDescriptionGrade scaleHPStatusFrom periodTitle
0002AssignmentsG U 3 4 57.50MandatoryA13

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established
by Department of Applied Physics and Mechanical Engineering 23 Feb 2010

Last revised
by Head Faculty Programme Director Niklas Lehto 17 Feb 2021