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.
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
(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 Oranization 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
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.