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Syllabus for

 Academic year
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)
FCMAS MSc PROGRAMME IN COMPLEX ADAPTIVE SYSTEMS, Year 1 (compulsory)
TKEFA CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 4 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING - Other elective courses, Year 4 (elective)

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.


Page manager Published: Thu 03 Nov 2022.