Physics of Complex Systems: Dynamics and Chaos

Course manual 2023/2024

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"

• Lecture notes and specialized references will also be available

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

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 25% of the final grade. Late submissions will be penalized. 

Mini-project:

Working in pairs 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. The mini-project accounts for 25% 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

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• Greg Stephens

Staff

• Ebo Peerbooms MSc