Course - Nonlinear Dynamics - FY8910
FY8910 - Nonlinear Dynamics
About
New from the academic year 2014/2015
Examination arrangement
Examination arrangement: Written examination
Grade: Passed/Failed
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| Skriftlig | 100/100 | 4 timer |
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 students will improve their 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.
Compulsory assignments
- Exercises
Recommended previous knowledge
Basic university level physics and mathematics. The course is suitable for students in other departments, provided they have a good background in mechanics and mathematics.
Course materials
Steven H. Strogatz: Nonlinear Dynamics and Chaos.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| TFY4305 | 7.5 |
Version: 1
Credits:
7.5 SP
Study level: Doctoral degree level
Term no.: 1
Teaching semester: AUTUMN 2014
Language of instruction: English, Norwegian
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- Physics
Examination
Examination arrangement: Written examination
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Autumn ORD Skriftlig 100/100 2014-12-13 09:00
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Room Building Number of candidates - Spring ORD Skriftlig 100/100
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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"