Self-Organization: Theory and Simulations

C. Gros, winter-term 2022/23

Corona notes

An online course is currently not planned.


A key concept in the theory of 'Complex and Adaptive Dynamical Systems' (CADS) is the notion of self-organization, namely that relatively simple basic evolution equations may give rise to complex spatio-temporal patterns and dynamical structures. For an online simulator of the Gray-Scott reaction diffusion system and a wide palette of other online simulations see complexity explorables

The course will start with an introduction to dynamical system theory and to bifurcation and catastrophe theory. Further topics will include the Turing instability and pattern formation in diffusion-reaction systems, swarm intelligence, opinion dynamics, car following models and Darwinian evolution (error-catastrophe, quasi-species, hyper-cycles).

A requirement for course completion is a student simulation project, which may be performed either alone or in groups of up to three students. The subject can be either of one's own choice or selected from a list that will be provided.

Depending on the programming knowledge of the course participants a short introduction to C++ will be given. This will be decided in the first week.


This lecture course is suitable for all students enrolled in physics/neurosicences/informatics/biology courses starting from the third year. Basic knowledge of differential equations and probability theory is helpful.


problem session
special data

javascript tutorial
Tue 8:30-10:00, Phys. 1.114
Fri 8:30-10:00, Phys. 1.114

Thu 14:00-16:00, Phys 01.310
Wed, Dec 21 2022, 14:00-16:00, Phys 01.120

Wed 15:00, Phys 01.120 (cip pool; Zoom link)
start: Tue, Oct 18

start: Thu, Oct 27

Dec 07 (only once)
the problem session and the computer lab include the possibility
for small research projects und student seminars
» Schein für ein Arbeitsgruppenseminar (BA/MA) möglich «
requirements for a certificate (als Wahlpflichtfach mit 8 CP):
  • attend problem sesssions, do exercises
  • develop and present a simulation project
  • Daniel's javascript page may help for the projects
  • oral exam (wenn benotet, ansonsten nicht)
  • Lehrevaluation: Dienstag, 31.01.2023 (pdf).


Monday to Monday cycle. If you have any question just contact

Lecture Notes

  1. Bifurcations and Chaos
  2. Epidemiological Modeling
  3. Adaptive Systems
  4. Self Organization and Pattern Formation
  5. Cellular Automata and Self-Organized Criticality
  6. Darwinian Evolution, Hypercycles and Game Theory
  7. ..
  8. Network Theory (only Chap. 1.2.2 Probability Generating Function Formalism)

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