Course - Nonlinear Dynamics - TFY4305
TFY4305 - Nonlinear Dynamics
About
Examination arrangement
Examination arrangement: School exam
Grade: Letter grades
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| School exam | 100/100 | 4 hours | C |
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 workload in the course is 225 hours.
Compulsory assignments
- Exercises
Further on evaluation
Written exam. The re-sit examination may be changed from written to oral.
Recommended previous knowledge
Basic university level physics and mathematics. The course is suitable for students interested in experiments, numerics or theory. The course is also suitable for students in other departments, provided they have a good background in basic mathematics and physics including basic mechanics.
Course materials
Steven H. Strogatz: Nonlinear Dynamics and Chaos.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| SIF4088 | 7.5 | ||
| FY8910 | 7.5 | AUTUMN 2014 |
No
Version: 1
Credits:
7.5 SP
Study level: Second degree level
Term no.: 1
Teaching semester: SPRING 2025
Language of instruction: English
Location: Trondheim
- Biology
- Physics
- Chemistry
- Mathematics
- Mechanics
Examination
Examination arrangement: School exam
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD School exam 100/100 C INSPERA
-
Room Building Number of candidates - Summer UTS School exam 100/100 C INSPERA
-
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"