Number of hours
- Lectures 16.5
- Projects -
- Tutorials 16.5
- Internship -
- Laboratory works -
- Written tests -
ECTS
ECTS 3.0
Goal(s)
The theory of dynamical systems makes it possible to predict, understand and control the evolution of complex phenomena modelled by a set of differential equations. Differential equations models arise naturally in numerous domains such as biology, electronics, mechanics… The goal of this course is to introduce the bases of this theory. Illustrations are given through various examples.
Responsible(s)
Guillaume JAMES
Content(s)
1. Introduction to dynamical systems, modelling using differential equations.
2. Existence and uniqueness of solutions of differential equations.
3. Linear dynamical systems: generalities, planar systems, hyperbolic systems.
4. Lyapunov stability.
5. Local study of nonlinear dynamical systems
Applied Analysis (1st year).
Test
Written exam
- MCC en présentiel **
N1 = examen écrit
N2 = examen écrit
- MCC en présentiel **
- MCC en distanciel **
N1 = devoir à la maison
N2 = devoir à la maison
- MCC en distanciel **
Calendar
The course exists in the following branches:
- Curriculum - Math. Modelling, Image & Simulation - Semester 7
Additional Information
Course ID : 4MMSD6
Course language(s): 
The course is attached to the following structures:
You can find this course among all other courses.
Bibliography
P. GLENDINNING: Stability, Instability and Chaos: an Introduction to the Theory of Nonlinear Differential Equations, Cambridge University Press, 1994.
J.H. HUBBARD, B.H. WEST: Differential Equations: A Dynamical Systems Approach, Springer, 1995.
E.D. SONTAG: Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer, 1998.