Nonlinear dynamical systems

linma2361  2018-2019  Louvain-la-Neuve

Nonlinear dynamical systems
5 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Absil Pierre-Antoine;
Language
English
Prerequisites
Background in calculus and linear algebra (level of LFSAB1101 and LFSAB1102)
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.
Aims

At the end of this learning unit, the student is able to :

1

Contribution of the course to the program objectives :

  • AA1.1, AA1.2, AA1.3
  • AA5.5, AA5.6

At the end of the course, the student will be able to:

  • Make adequate use of basic mathematical tools to model, analyze, and design nonlinear dynamical systems, in areas such as neurodynamics, nonlinear control, and physics.

Transversal learning outcomes :

  • Use a reference book in English;
  • Discuss and criticize research articles ;
  • Report in writing and present the results orally.
 

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
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
  • Homeworks, exercices, or laboratory work during the course semester
  • Written report and oral presentation of a project, including a bibliographical part (article or book chapter reading) and computer illustrations of the theory.
Precisions are given in the course outline (plan de cours) available on iCampus > LINMA2361 > Documents et liens
Online resources
http://moodleucl.uclouvain.be/course/view.php?id=8235
Bibliography
  • Ouvrage de références
  • Documents complémentaires disponibles sur Moodle
Des précisions sont fournies dans le plan de cours disponible sur Moodle.
Faculty or entity
MAP


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Electro-mechanical Engineering
ELME2M
5
Master [120] in Biomedical Engineering
GBIO2M
5
Master [120] in Physics
PHYS2M
5
Master [120] in Mathematical Engineering
MAP2M
5