TFY4305 - Nonlinear Dynamics


Examination arrangement

Examination arrangement: Home examination
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
Home examination 100/100 4 hours

Course content

Graphical solution methods for non-linear differential equations. Phase portraits, fixed point analysis, bifurcations, limit cycles, strange attractors, Poincare and Lorenz maps, multiscale perturbation theory. Iterative maps. Period doubling, chaos, scaling and universality. Fractals. Physical examples.

Learning outcome

The course is an introduction to nonlinear systems and chaos. The student is expected to acquire basic knowledge of nonlinear differential equations and iterative maps. The student is capable of
finding fixed points and determine their stability, analyze the various types of bifurcations in one dimension (saddle node, transcritical, and pitchfork) and two dimensions (homoclinic, degenerate, and Hopf), draw bifurcation diagrams and stability diagrams. For two-dimensional systems, the student is able to draw phase portraits and find basins of attraction. Moreover, the student is able to analyze limit cycles and their stability.
The student can analyze discrete maps, find their fixed points and
understand the mechanism behind period doubling. The student has basic knowledge of the most important fractals, and their topological and metric properties. Similarly, the student knows about the properties of the most important strange attractors in discrete and continuous time. The student will improve communication skills by solving problems on the blackboard and training in solving nonlinear problems using numerical methods.

Learning methods and activities

Lectures and problem sessions. All students will go through a set of exercises on the blackboard during the semester, to be allowed to take the exam. In addition, all students must solve a numerical assignment and hand in a report. Expected work load in the course is 225 hours.

Compulsory assignments

  • Exercises

Further on evaluation

The re-sit examination may be changed from written to oral.

Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

Course materials

Steven H. Strogatz: Nonlinear Dynamics and Chaos.

Credit reductions

Course code Reduction From To
SIF4088 7.5
FY8910 7.5 01.09.2014
More on the course

Version: 1
Credits:  7.5 SP
Study level: Second degree level


Term no.: 1
Teaching semester:  AUTUMN 2020

No.of lecture hours: 3
Lab hours: 1
No.of specialization hours: 8

Language of instruction: English

Location: Trondheim

Subject area(s)
  • Biology
  • Physics
  • Chemistry
  • Mathematics
  • Mechanics
Contact information
Course coordinator: Lecturer(s):

Department with academic responsibility
Department of Physics



Examination arrangement: Home examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam Room *
Autumn ORD Home examination 100/100

Release 2020-12-17

Submission 2020-12-17

Release 09:00

Submission 13:00

Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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