Complex and Adaptive Dynamical Systems

C. Gros, summer-term 2019


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 full (Passwort: CADS) are freely available. For the exercises please consult the printed version.

Since 2008 (second/third/fourth edition 2010/2013/2015) the entire course is available as a Springer textbook .

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, Phys. 01.114
Fri 10-12, Phys, 01.114
start: Tue, Apr. 16, 2019
problem session Tue 8-10, Phys. 01.114
Fri 12-14, Phys. 01.144 (new)
start: Tue, Apr. 23, 2019
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
  • Evaluation der Vorlesung am 02.07.2019, 10:00 - 12:00 Uhr


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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