Dynamical systems are characterized by a state that evolves in time and play an essential role in many fields of application of mathematics, such as exact sciences (physics, chemistry, biology), computer science or economics and management.
At the end of this course, the students will be able to model simple dynamical phenomena, simulate them on a computer, and use the main mathematical tools to study their behavior.
Provide an introduction to mathematical modeling, nonlinear system analysis, and stochastic processes.
The course is pluridisciplinary and will address the student's interests in his/her favourite subject or in general. Theoretical notions will be illustrated with many concrete examples (biological mechanisms, electricity, neuroscience, etc.).
A first part of the course will introduce the different types of dynamical systems and basic notions (state space, trajectory, attractor). It will also cover the main system modeling techniques (natural laws, linearization).
The second part of the course will provide an introduction to basic notions and mathematical tools for studying dynamical systems: phase portrait, cobweb diagram, equilibrium point, local and global stability.
The last part will focus on the study of stochastic systems. In the case of discrete process, Poisson process will ne investigated in details, and then generalized through the master equation. An introduction to Markov processes and queuing theory will also be provided. Finally, continuous processes will be considered though basic stochastic calculus and the Fokker-Planck equation.
The evaluation will consist of two distinct parts: (1) modeling of a dynamical system and questions of analysis (written); (2) analysis and numerical simulation (with a computer).
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Bachelier en sciences mathématiques | Standard | 0 | 5 |