Nonlinear dynamical systems [ LINMA2361 ]

> https://icampus.uclouvain.be/claroline/course/index.php?cid=INMA2361

LFSAB1102 (Mathématiques 2) : basic notions in topology, linear operators, linear differential equations with constant coefficients, unconstrained optimization, and vector calculus.
LFSAB1106 (Mathématiques appliquées : signaux et systèmes) : basic notions in signals and systems, including state space representation and stability

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.

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.

• 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

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

• 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

• Reference book
• Complementary documents posted on iCampus

Precisions are given in the course outline (plan de cours) available on iCampus.