Introduction to dynamical systems

 Faculteit Medische Wetenschappen / UMCG Jaar 2021/22 Vakcode BWM142 Vaknaam Introduction to dynamical systems Niveau(s) master Voertaal Engels Periode semester II a ECTS 5

Uitgebreide vaknaam Introduction to dynamical systems
Leerdoelen The study of human movement is unthinkable without (knowledge of) dynamics, as obviously movement implies ‘change over time’. In this course, the student will therefore be introduced into the field of linear and non-linear dynamical systems with reference to the study of human motor behaviour and acquires elementary understanding of fundamental mathematical principles, concepts and methods. The student further learns to adopt this through model based computer simulations using Matlab/Simulink. The course builds up towards abstract scientific thinking.
At entry, the student should at least have some elementary (‘high-school’) acquaintance of physics and mathematics (algebra, differential and integral calculus). Furthermore, it is prerequisite to have some initial experience with coding (preferably in Matlab). If not: it is expected that the prospective student familiarize herself/himself before the start of the course, for instance through the Matlab ‘Getting Started’ tutorial, and/or via a fellow student.
Omschrijving The lectures cover theoretical issues (e.g., metaphysics, analytical and numerical mathematics) alongside illustrative examples with regard to the contents in the course material (see literature). These issues will subsequently be applied and practiced in individually executed practical assignments.
Issues that will be studied are:
- What is a ‘dynamical system’?
- Exact and numerical methods of dynamical analysis
- Introduction to Simulink (the simulation environment of Matlab)
- Analysis of (non-)linear dynamical systems: Differential equations, transformations, state/phase description, fixed points, stability, potential functions, Lyapunov functions, etc.
- Effects of feedback and coupling, parameter changes, and noise.
- Non-linear dynamics: limit cycles, time scales, complex behaviour etc.
Uren per week
Onderwijsvorm hoor- en werkcolleges en practica
(Lectures (14), practical sessions (28) (either physical or online))
Toetsvorm verslag en presentatie
(Written assignment(s) or written exam (depending on the number of participants))
Vaksoort Master
Coördinator dr. H.J. de Poel
Docent(en) dr. H.J. de Poel
Verplichte literatuur
Titel Auteur ISBN Prijs
- Selected chapters from Fuchs, A. (2013). Nonlinear dynamics in complex systems: theory and applications for the life-, neuro- and natural sciences. Berlin; Heidelberg: Springer.
- Additional book chapters and articles, t.b.a. in the course guide.
Entreevoorwaarden At entry, the student should at least have some elementary (‘high-school’) acquaintance of physics and mathematics (algebra, differential and integral calculus). Furthermore, it is prerequisite to have some initial experience with coding (preferably in Matlab). If not: it is expected that the prospective student familiarize herself/himself before the start of the course, for instance through the Matlab ‘Getting Started’ tutorial, and/or via a fellow student.
Opmerkingen Minimum number of participants: 5
Because of the limited capacity of this course there will be a selection procedure. Therefore each prospective student has to write a letter of motivation and submit this no later than 1 month before the start of the course. This letter should contain: list of master courses followed and intended, reason for wanting to follow this course, link to research project and ‘Master Plan’ and a statement regarding ability in the knowledge and skills prerequisites outlined above. The lecturer will assess the motivation letter before the student is permitted to enrol in the course. There will be given priority to M1 students.
Opgenomen in
Opleiding Jaar Periode Type
MSc Human Movement Sciences 1 semester II a keuze
MSc Sport Sciences 1 semester II a keuze