Complex Systems; 5A1352

Course for F4 and graduate students. Lectures autumn 2000, period 1.
                                                            Begins Tuesday 5 September 14-16, room F 13,  (Sing-Sing, Lindstedsvägen 30)
                                                           Continues Friday 8 September 10-12, Room F11.

                                                  Week 37:  Tuesday  12/9    14-16      F51
                                                                      Friday   15/9      8-10      E2      Note time and place

                                                 Week 38:   Tuesday  19/9    14-16   F11
                                                                       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                10-12  Q14
                                                    Friday                       13/10    10-12  Q2    Note place

Exercises autumn 2000: 1-4:   postscript format      number 5; postscript
                                              pdf format                 number 5; pdf
 Exercises are to be finished Tuesday 14 November. Then, I will discuss them and show solutions in room Q23, 14-16

                   For information 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.