Duration
26h Th, 26h Pr
Number of credits
| Master of Science (MSc) in Biomedical Engineering | 5 crédits | |||
| Master of Science (MSc) in Electrical Engineering | 5 crédits |
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
The course is an introduction to nonlinear systems dynamics and to the mathematical tools for studying them. The course is pluridisciplinary and addresses the student's interests in his/her favourite subject or in general.
The main aspects and results from dynamical systems theory will be covered:
- stability of equilibria and limit cycles
- phase portraits
- bifurcations and singularities
- chaos theory, strange attractors, and fractals
- etc.
See also the webpage: http://sites.google.com/site/gdrion25/teaching/syst0017
Learning outcomes of the learning unit
At the end of this course, the student will know the main dynamical behaviors exhibited by nonlinear systems (equilibria, periodic behaviors, chaotic phenomena, etc.). He/she will master the mathematical concepts and techniques required to study these behaviors: phase portrait analysis, trajectory simulation, fixed point computation, stability analysis, bifurcation diagrams, etc. In addition, the student will be able to use the relevant tools on computer (Matlab).
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, II.3, III.1, III.2, IV.1, VI.1, VII.1, VII.2, VII.3, VII.4, VII.5 of the MSc in biomedical engineering.
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, II.3, III.1, III.2, IV.1, IV.8, VI.1, VII.1, VII.2, VII.3, VII.4, VII.5 of the MSc in electrical engineering.
Prerequisite knowledge and skills
SYST0002-1 or an equivalent course on linear systems
Planned learning activities and teaching methods
The course is based on 2h ex-cathedra lectures on theoretical concepts. These lectures will be illustrated with concretes examples from various scientific fields. Three lessons will be dedicated to the application of the theoretical concepts to the analysis of neuronal excitability.
The lectures are meant to encourage active student participation. The student will be invited to give an oral presentation of their personnal project during the semester.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face.
Recommended or required readings
Textbook:
'Nonlinear Dynamics and Chaos: with applications to Physics, Biology, Chemistry and Engineering', Steven H. Strogatz, Perseus Publishing, 2001.
Individual project on a specific application chosen according to the student's preferences, including an oral presentation during the semester and a final report at the end of the semester.
See also the course webpage
http://sites.google.com/site/gdrion25/teaching/syst0017
Work placement(s)
Organizational remarks
A detailed schedule can be found on page http://sites.google.com/site/gdrion25/teaching/syst0017
Contacts
G. Drion (gdrion@ulg.ac.be, Bldg. B28, office I140)