Complex and Adaptive Dynamical Systems

C. Gros, summer term 2021

Online course

The course will be fully online. Details of the organization, including the Zoom links, will be given here before the start.


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 10-12 (online)
Fri 10-12 (online)
start: Tue, Apr. 13, 2021
problem session Fri 12-14 (online) start: Tue, Apr. 16, 2021
requirements for a certificate (als Wahlpflichtfach mit 8 CP):
  • attend problem sessions, do exercises (60%);
    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.
  • for a grade (benoteter Schein) there will be oral exams


If you have any questions just contact
  • Fabian Schubert click to show email
  • Oren Neumann click to show email
Fabian and Oren are in office 01.141
  • ...

Lecture Notes

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