Complex and Adaptive Dynamical Systems - Claudius Gros

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.

Zoom link for the lecture:
https://uni-frankfurt.zoom.us/j/91554812655?pwd=Q2xuZkNtblNyTExmR0hBNU1DMXVLZz09
Zoom link for the tutorial:
https://uni-frankfurt.zoom.us/j/96736202350?pwd=NmRyK1hKM1FqM21QUldudENyNzd1Zz09
changed course times: Fridays: 9:30-11:00
handing in of exercises: upload to your NextCloud folder; a single pdf file, plus code files
naming of files: 'ex1_name.pdf', etc.

Attendences to to the tutorials is mandatory. Please turn your video on when interacting (discussions, questions, ..).

Lehrevaluation: Tuesday, June 22: link

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

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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