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 and nonlinear system analysis.
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 (Lagrange fomalism, 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, stability, periodic orbits and limit cycles.
The evaluation will consist of two distinct parts: (1) modeling of a dynamical system and small questions of analysis (written); (2) analysis and numerical simulation (with a computer).