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| SYST0017-1 | Non linear systems
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| Duration : | 30h Th, 30h Pr |
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| Number of credits : |
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| Lecturer : | Rodolphe Sepulchre |
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| Substitute(s) : | Alexandre Mauroy |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, review in January |
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Course contents :
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| The course is an introduction to the behaviors of nonlinear systems and to the mathematical tools for studying them. The course is pluridisciplinary and will address the student's interests in his/her favourite subject or in general.
The main aspects and results from dynamical systems theory will be covered:
- phase portaits
- stability of equilibria and limit cycles
- bifurcation diagrams
- discrete maps and ergodicity
- chaos theory, strange attractors, and fractals
- etc.
Theoretical notions will be illustrated with many concrete examples (biological mechanisms, electricity, neuroscience, meteorology, etc.). Specific applications will be studied through individual projects. The course will also introduce current research topics in dynamical systems theory.
See also the webpage:
http://www.montefiore.ulg.ac.be/systems/SYST017/syst017.htm |
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Learning outcomes of the course :
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| 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). |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| SYST002-1 or an equivalent course on linear systems |
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Planned learning activities and teaching methods :
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| The course is based on 2h ex-cathedra lectures on theoretical concepts. These lectures will be illustrated with a few short exercices and concretes examples from various scientific fields.
The lectures are meant to encourage active student participation. The student will be invited to give a 10min oral presentation on a chosen section in the reference textbook, according to his/her own preferences. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face. |
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Recommended or required readings :
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| Textbook:
'Nonlinear Dynamics and Chaos: with applications to Physics, Biology, Chemistry and Engineering', Steven H. Strogatz, Perseus Publishing, 2001. |
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Assessment methods and criteria :
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| During the school year:
2-3 short homeworks + 1 short oral presentation (10 min) on a chosen subject in the reference textbook.
At the end of the course:
individual project on a specific application chosen according to the student's preferences (written report + oral presentation). See also the course webpage
http://www.montefiore.ulg.ac.be/systems/SYST017/syst017.htm |
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Work placement(s) :
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Organizational remarks :
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| A detailed schedule can be found on page http://www.montefiore.ulg.ac.be/systems/SYST017/syst017.htm |
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Contacts :
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| A. MAUROY (a.mauroy@ulg.ac.be, Bldg. B28, office I140) |
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