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.
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).
Written exam (2 h) (E).
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.