Complex and Adaptive Dynamical Systems

C. Gros, summer-term 2015

Content

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 edition 2010/2013) the entire course is available as a Springer textbook .

Table of Contents

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

Requirements

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. 14, 2015
problem session Wed 8-10, Phys. __.102
start: Wed, Apr. 22, 2013
problem session includes possibility for small research projects und student seminars
» Schein für ein Arbeitsgruppenseminar (BA/MA) möglich «
requirements for a certificate (als Wahlpflichtfach mit 8 CP):
  • attend problem sesssions, do excerises
  • a short seminar (about 20min) on a topic of your choice during the tutorials:
    suggestions for seminar topics .
    Schedule for the talks.
  • dates for oral exams (sign up with Mrs. Kolokotsa, 01.131)
    • Tuesday, July 28
    • Tuesday, October 6

Exercises

If you have any question just contact
  • Bulcsu Sandor (sandor@nirvana.org, spam@itp.uni-frankfurt.de)
  • Hendrik Wernecke (wernecke@nirvana.org, spam@itp.uni-frankfurt.de)
Bulcsu and Hendrik (both are in the office 01.141) will also help you to find a subject for your seminar.

Lecture Notes



Claudius Gros
April, 2015