5.00 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Absil Pierre-Antoine; Massart Estelle;
Language
English
> French-friendly
> French-friendly
Prerequisites
Background in calculus and linear algebra (level of LEPL1101 and LEPL1102)
Main themes
The course is an introduction to the analysis and synthesis of nonlinear dynamical systems. The mathematical tools are illustrated on different applications, preferentially in the fields of neurodynamics, nonlinear control, and physics. Further specific illustrations are presented by the students at the end of the course.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 |
Contribution of the course to the program objectives :
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Content
- Introduction to nonlinear phenomena
- Multiple equilibrium points and systems in the plane
- Lyapunov functions, gradient systems, stability
- Limit cycles
- Hopf bifurcations, asymptotic methods
- Introduction to chaos
Depending on the choice of the course book, some of the following themes may also be touched :
- Introduction to dynamical models in neuroscience
- Simple neural computation models, Hopfield networks
- Stabilization of equilibrium points
- Coupled oscillators, synchronization phenomena, and collective motions
- Input-output tools for nonlinear system analysis
Teaching methods
- Lectures.
- Homeworks, exercices, or laboratory work to be carried out individually or in small groups.
Evaluation methods
- Work carried out during the term: homework assignments, exercises, or laboratory work. These activities are thus organized (and evaluated) only once per academic year.
- Exam: written report and oral presentation of a project, including a bibliographical part (article or book chapter reading) and computer illustrations of the theory.
Further information is provided in the "Course outline" document available on Moodle (see "Online resources" below).
Online resources
Bibliography
- Textbook
- Complementary notes posted on Moodle
Faculty or entity
MAP
