Course for F4 and graduate students. Lectures autumn 2000, period 1.
Complex Systems; 5A1352
Begins Tuesday 5 September 14-16, room F 13, (Sing-Sing, Lindstedsvägen
Continues Friday 8 September 10-12, Room F11.
Week 37: Tuesday 12/9 14-16
Friday 15/9 8-10
E2 Note time and place
Week 38: Tuesday 19/9 14-16
Friday 22/9 10-12 Q32 Note
time and place
Tuesdays 26/9, 3/10 10/10 14-16 Q13
Fridays 29/9, 6/10
13/10 10-12 Q2 Note place
Exercises autumn 2000: 1-4: postscript
number 5; pdf
Exercises are to be finished Tuesday 14 November. Then, I will
discuss them and show solutions in room Q23, 14-16
about the exercises. press here
Course may be given in English.
Lecturer: Clas Blomberg, Theoretical Physics, phone 08-790 7176, email
'Complex systems' has become a collective title for a discipline of the
study of physical systems, not necessarily complicated, that are governed
by non-linear equations and give rise to complex features. Examples of
such features are various ordered processes and structures such as non-linear
oscillations and waves as well as disordered chaotic processes and fractal
structures. There are applications within all regions of physics, but this
subject has, maybe, become most noted for the possibility to create spontaneous
order and what is called self-organization with application to biology
and questions about the evolution of life. The course is intended as a
general introduction to this subject and the study of the mathematical
equations that are behind it.
Coupled, non-linear equations. Characterization of singular points with
stability analysis. Limit cycles, chaotic attractors. Characterization
of chaotic processes. Examples. Fractal structures. Julia- and Mandelbrot
sets. Chaotic attractors and fractals. Various fractal dimensions, multifractals.
Analysis of chaotic time series. Controlling chaos. Brief description of
conservative systems and KAM-properties. Non-linear partial differential
equations. Spatial structures: Non-linear waves, solitons. Cellular automata.
Applications. Discussion about biological relevance.
Solution of exercises, mainly of computer laboratory type, which are to
be discussed with the examinator (INL1;4cr).
Information about the exercises will be linked to this site and regualrly
updated to the link above.
Own material. Cost 50:-
E.A.Jackson, Perspectives of nonlinear dynamics, Cambridge University
Press, 2 parts, 1990. At present out of print.
More extensive literature list will be given during the course.