Self-Organization: Theory and Simulations

C. Gros, summer-term 2020

Corona notes

Summer term SS20, lecture and tutorials will take place online.
  • The course will start Tuesday April 21st.
  • Please send an email to Fabian (see below) if you intend to participate.
  • Informations will be posted here in time.
  • yes, epidemic models will be treated!

online course organization for SS20
general Students are expected to study the online course material on their own.
lecture chat Twice a week, Tuesdays and Fridays 10:00, there will be a lecture chat with Zoom.
Time to ask questions. Key or interesting points of the course material will be discussed.
lecture chat link
|7|4|1|9|2|0| (in case you need the password)
milestonescourse material to study
till June 26: including Chap. 5.3.2
till June 19: including Chap. 4.4.2
till June 12: including Chap. 4.2.3
till June 05: including Chap. 4.1
till May 29: including Chap. 3.3.1
till May 22: including Chap. 3.1.4
till May 15: including Chap. 3.1.1
till May 8: including Chap. 2.2.1
till May 1: including Chap. 1.4   (normal lecture on May 1st)
till April 24: including Chap. 1.2.2
problem sheets problem sheets are posted online (see below), starting the first week
tutorial link
  • for handing in (uploading) student solutions
  • for questions forum
  • sample solutions will be available here
tutorial chatwill be organized twice a week, every Tuesday 14:00 and Thurday 10:00


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
Wed 9:15-11:00, Phys. __.401
Thu 9:15-11:00, Phys. __.401

Tue 10:15-12:00, Phys. 01.114
Fri 10:15-12:00, Phys. 02.114
start: Wed, April 15 2020
(modulo Corona) 

start: (tba)
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):


Monday to Monday cycle. If you have any question just contact
  • Oren Neumann (,; Phys 01.141
  • Fabian Schubert (,; Phys 01.141
  • Lukas Schneider (,; Phys 01.218

Lecture Notes

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

Project Presentations




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