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Invariant Set of the Lorenz System Show image information
Attractor of the Mackey-Glass Equation Show image information
Unstable manifold of the Kuramoto-Sivashinsky equation Show image information
Petersen Graph Show image information

Invariant Set of the Lorenz System

Attractor of the Mackey-Glass Equation

Unstable manifold of the Kuramoto-Sivashinsky equation

Petersen Graph

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

Contact: Adrian Ziessler

The University for the Information Society