Nonlinear dynamical systems

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.

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

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

• Lectures.
• Homeworks, exercices, or laboratory work to be carried out individually or in small groups.

Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

• 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