Physics of Complex Systems: Dynamics and Chaos

Course manual 2024/2025

Course content

This course forms part of a curriculum in complex systems and will  focus on dynamical systems, especially but not exclusively from the viewpoint of  statistical physics.  We will cover the following subjects:

1. Low-dimensional dynamical systems with regular attractors: fixed points, limit cycles and bifurcations
2. Linear stability analysis
3. Low-dimensional dynamical systems with irregular attractors: chaos
4. Variability as entropy: KS-entropy, sequence entropy and information theory
5. Variability from partial information: delay embeddings and Taken's theorem

Contemporary research directions will be explored through extended exercises that include a computational component and are motivated by particular analysis techniques.  Students should expect computational exercises that involve numerical simulations and analysis.

Study materials

Literature

• Steven H Strogatz, "Nonlinear Dynamics and Chaos" (main textbook)

• Lecture notes and specialized references will also be available

• Stephen Wiggins "Introduction to Applied Dynamical Systems and Chaos"  (advanced supplementary textbook)

Software

• MATLAB, Python, Mathematica or computational language of choice

Objectives

• Understand and apply various concepts and tools of statistical physics, dynamical systems and information theory to problems in complex systems.
• Understand how complex phenomena can arise even from simple theoretical descriptions, and how this influences the scientific methodology of our investigation.
• Understand the interplay between theoretical ideas and data derived from precision experiments, including computational experiments. Leverage this understanding to derive new knowledge of complex systems.

Teaching methods

• Lecture
• Self-study
• Working independently on e.g. a project or thesis

Learning activities

Attendance

Requirements concerning attendance (OER-B).

Assessment

The course assessment is computed from the sum: Exercise 1 (20 pts) + Quiz I (10 pts) + Quiz II (30 pts) + Mini-Project (40 pts).

Inspection of assessed work

Partial grades are announced on Canvas as soon as they are available

Assignments

Exercises:

Students will complete two exercise assignments that involve both analytical and computational work. These are to be carried out individually, although relevant group discussions are encouraged. The assignments should be submitted by the specified deadlines. The first assignment will not be given a grade and will simply form a basis for discussion and review with the student. The second assignment accounts for 20% of the final grade. Late submissions will be penalized. 

Mini-project:

Working in groups or alone, students will complete a mini-project, exploring a topic in depth taken either from a list of suggestions, or a new topic from the students themselves (the latter requires approval from the course coordinator).  A mini-project overview is provided with examples of concrete computational exercises.  Students will submit a Jupyter notebook (or equivalent), detailing their computations and any important contextual information, and will also make a short  recorded “pitch” video.  These should be less than 10 minutes and will be shared with other students in the course.  The video is a chance to present the mini-project and should include background such as “why is your project interesting?" and "how does your project fit with BIG questions?”, as well as an explanation of what you did, and finally what you found.  These can, for example, be easily created from a Zoom recording. The mini-project accounts for 40% of the grade. Late submissions will be penalized. 

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Contact information

Coordinator

• Greg Stephens

Staff

• Ebo Peerbooms MSc