Infinite Dimensional Dynamical Systems

Development of a set-oriented numerical technique which allows to compute low-dimensional invariant sets for infinite dimensional dynamical systems.

Systems of interest:

Delay Differential Equations (DDEs): type of differential equation in which the time derivative of the unknown function depends not only on the current state but also on previous times.
Focus of interest: Analysis of long term behavior of DDEs
Applications: e.g. signal processing, disease transition, population models

Successively finer coverings of a relative global attractor for the Mackey-Glass equation

Partial Differential Equations (PDEs): type of differential equation in which the time derivative of the unknown function depends on multivariable functions and their partial derivatives.
Focus of interest: Analysis of long term behavior of PDEs
Applications: e. g. fluid dynamics, quantum mechanics, electrodynamics

Box covering of an attractor of the Kuramoto Sivashinsky equation