Complex and Adaptive Dynamical Systems

C. Gros, summer-term 2017


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 (uncorrected) lecture notes on CADS are freely available (of the old, second edition). For the solutions of the exercises please consult the printed book on CADS.

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 Oranizattion 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/neurosicences/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
Thu 13-15, Phys, 01.114
start: Tue, Apr. 18, 2017
problem session Thu 15-17, Phys. 02.201b (changed)
start: Thu, Apr. 27, 2017
requirements for a certificate (als Wahlpflichtfach mit 8 CP):
  • attend problem sesssions, do excerises (60%);
    working in groups of 1-3 possible
  • you may present a short research seminar (about 20min)
    on a topic of your choice at the end of the course,
    counting for up-to 15% of execerises
    suggestions for seminar topics.
  • dates for oral exams (sign up eventually with Mrs. Metz, 01.131)
    • late July / early August
    • late September / early October


If you have any question just contact
  • Philip Trapp click to show email
  • Hendrik Wernecke click to show email
Hendrik is in office 01.141 and Philip in office 01.217

Lecture Notes

Claudius Gros