Aller au menu Aller au contenu
Une voie, plusieurs choix
Informatique et Mathématiques appliquées
Une voie, plusieurs choix

> Formation > Cursus ingénieur

DYNAMICAL SYSTEMS

A+Augmenter la taille du texteA-Réduire la taille du texteImprimer le documentEnvoyer cette page par mail cet article Facebook Twitter Linked In
  • Number of hours

    • Lectures : 36.0
    ECTS : 2.5

Goals

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.


Contact Antoine GIRARD

Content

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



Prerequisites

Applied Analysis (1st year).

Tests

Written exam (2 h) (E).



N1=E1
N2=E2

Additional Information

Curriculum->MMIS.->Semester 4

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.

A+Augmenter la taille du texteA-Réduire la taille du texteImprimer le documentEnvoyer cette page par mail cet article Facebook Twitter Linked In
Université Grenoble Alpes