Complex and Adaptive Dynamical Systems

C. Gros, summer term 2026

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 lecture notes are posted further down. You may also consult the corresponding textbook
Complex and Adaptive Dynamical Systems: A Comprehensive Introduction .

Table of Contents

  • Chapter 1: Network Theory
  • Chapter 2: Bifurcations and Chaos in Dynamical Systems
  • Chapter 3: Dissipation, Noise and Adaptive Systems
  • Chapter 4: Self Organization
  • Chapter 5: Information Theory of Complex Systems
  • Chapter 6: Self-Organized Criticality
  • Chapter 7: Random Boolean Networks
  • Chapter 8: Darwinian evolution, Hypercycles and Game Theory
  • Chapter 9: Synchronization Phenomena
  • Chapter 10: Complexity of Machine Learning
[ Complex and Adaptive Dynamical Sytems, a Comprehensive Introduction ]

Requirements

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 8:30-10:00, Phys __.401
Fri 8:30-10:00, Phys __.401 		start: Tue, Apr. 14, 2026
problem session Wed 14:15-16:00, Phys 02.120
(date/time can be changed) 		start: (second week)
requirements for a certificate (als Wahlpflichtfach mit 8 CP):
  • Attend problem sessions.
  • Exercises are handed out and may be discussed. There is no requirement for doing them.
  • 3 projects (theory and simulations; 3-4 weeks each) are mandatory. The results are presented during the respective problem session. Attendence is required.
  • For a grade (benoteter Schein) there will be oral exams.

Tutors

If you have any questions just contact
  • Daniel Nevermann; Phys 01.141 click to show email

Exercises / Projects

  • to be given

Lecture Notes


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