Complex and Adaptive Dynamical Systems

C. Gros, winter term 2023/24


Complex system theory deals with dynamical systems in a wide range of disciplines showing non-trivial and/or emergent properties.
This course provides the relevant core knowledge. It is suitable for all students having a basic math education.

Basic concepts and phenomena covered will include

  • network theory: small-world, scale-invariant, percolating
  • bifurcation theory, adaptive systems, deterministic chaos, strange attractors, catastrophe theory
  • information theory, Shannon entropy, mutual information, complexity
  • cellular automata, self-organized criticality
  • ...

Lecture notes and text book

The lecture notes are posted further down. You may also consult the corresponding textbook
Complex and Adaptive Dynamical Systems, a Primer .

Table of Contents

  • Chapter 1: Graph Theory and Small-World Networks
  • Chapter 2: Bifurcations and Chaos in Dynamical Systems
  • Chapter 3: Dissipation, Noise and Adaptive Systems
  • Chapter 4: Self Organization and Pattern Formations
  • Chapter 5: Complexity and Information Theory
  • Chapter 6: Cellular Automata and Self-Organized Criticality
  • Chapter 7: Random Boolean Networks
  • Chapter 8: Darwinian evolution, Hypercycles and Game Theory
  • Chapter 9: Synchronization Phenomena
  • Chapter 10: Elements of Cognitive System Theory
[ Complex and Adaptive Dynamical Sytems, a Primer ]


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

course Tue 8:30-10:00, Phys __.401
Fri 8:30-10:00, Phys __.401
(no lecture on first Friday, Oct 20.)
start: Tue, Oct. 17, 2023
problem session Fri 12:15-14:00, Phys 02.116 (Hilbert)
(date/time can be changed)
start: (second week)
requirements for a certificate (als Wahlpflichtfach mit 8 CP):
  • attend problem sessions, do exercises (70%);
    working in groups of up to two students is possible
  • you may do a project (theory and simulations) and present
    the results as a short research seminar (about 20min)
    at the end of the course, counting for 20% of exercises;
    suggestions for project topics
    (this is an old version that will be updated).
  • for a grade (benoteter Schein) there will be oral exams
  • Evaluation der Vorlesung an 23.01.2024, 8:00 - 10:00 Uhr


If you have any questions just contact
  • Daniel Nevermann; Phys 01.141 click to show email
  • Lutz Kiefer; Phys 02.111 click to show email


Lecture Notes

Legal note: We do not take any responsibility for the content of webPages linked here-in.
Bitte bachten Sie die Datenschutzerklärung