Complex and Adaptive Dynamical Systems

C. Gros, summer term 2021

Online course

The course will be fully online. Details will be explained in the first lecture/tutorial. Attendences to to the tutorials is mandatory. Please turn your video on when interacting (discussions, questions, ..).

Study objectives

  • till Monday, May 17
    Chapter: Epidemics
    --all--
  • till Monday, May 10
    Chapter: Bifurcations and Chaos in Dynamical Systems
    --all--
  • till Monday, May 03
    Chapter: Bifurcations and Chaos in Dynamical Systems
    1.3.1 Catastrophe Theory
  • till Monday, April 26
    Chapter: Graph Theory and Small-World Networks --- all
  • till Monday, April 19
    Chapter: Graph Theory and Small-World Networks
    1.2.2 Probability Generating Function Formalism

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 Primer .

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 ]

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 10:15-12:00 (online)
Fri 9:30-11:00 (online)
start: Tue, Apr. 13, 2021
problem session Fri 12:15-14:00 (online) start: Fr, Apr. 16, 2021
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

Exercises

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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