Use the search function to search amongst programmes at Chalmers. The study programme and the study programme syllabus relating to your studies are generally from the academic year you began your studies.
Syllabus for |
|
FFR130 - Dynamical systems |
|
Owner: FCMAS |
|
3,0 Credits (ECTS 4,5) |
Grading: TH - Five, Four, Three, Not passed |
Level: C |
Department: 16 - PHYSICS
|
Teaching language: English
Course module |
|
Credit distribution |
|
Examination dates |
Sp1 |
Sp2 |
Sp3 |
Sp4 |
|
No Sp |
0100 |
Examination |
3,0 c |
Grading: TH |
|
|
|
3,0 c
|
|
|
|
|
Contact examiner |
In programs
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TKEFA CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 4 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING - Other elective courses, Year 4 (elective)
FCMAS MSc PROGRAMME IN COMPLEX ADAPTIVE SYSTEMS, Year 1 (compulsory)
Examiner:
Professor Bernhard Mehlig
Eligibility:For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.
Aim
Simple deterministic systems can give rise to complex and unpredictable behavior. In a chaotic system, the distance between two close initial states grows exponentially with time, which makes the long-term behavior of the system impossible to predict. The purpose of the course is to give an understanding of basic theoretical aspects of nonlinear dynamical systems: how is chaos measured and characterised? How can one detect deterministic chaos in an experimental time series?
How can one control and predict chaotic systems? Applications in physics, biology (populations dynamics), and economics (prediction and non-linear time series analysis) are described.
Content
See course home page
Topics covered
- One-dimensional iterated maps: symbolic dynamics, in particular for the logistic map
- Ergodicity, Kolmogorov-Sinai entropy
- Lyapunov exponents
- Bifurcation theory. Structural stability.
- Iterated maps in more than one dimension. Attractors
- Fractal dimensions. Fractals in physical systems
- Space-time chaos. Cellular automata and coupled map lattices
- Non-linear time series analysis
- Control of chaotic systems
- Turbulence
Organisation
Lectures
Literature
E. Ott, Chaos in Dynamical Systems Cambridge University Press, 1993, and lecture notes which will be handed out.
Examination
Through homework problems during the course.
|
|