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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

Chair of Applied Mathematics

Professor Dr. Michael Dellnitz

The primary strength of this chair is the development of efficient algorithms for the numerical treatment of Dynamical Systems and Optimization Problems. Research activities concentrate on both theoretical aspects of these algorithms and their numerical realization.

Research activities:

  • Dynamical systems
  • Multiobjective optimization

Current research projects:

DFG Individual Research Grant: "Algorithms for swarms: Distributed Computing meets Dynamical Systems"

The goal of this project is to investigate the capabilities and limitations of local, distributed strategies for swarms of mobile robots. Such strategies consist of protocols run by the individual robots. They are supposed to guide the movements of the robots in such a way that globally a prescribed formation like gathering, forming a line or other shapes is reached from an arbitrary initial configuration of the robots. This research direction is well-established in distributed computing. Our approach is to combine techniques from distributed computing and dynamical systems research in order to enhance the understanding of protocols for such formation tasks. To this end, we analyze the speed of the protocols in terms of runtime complexity in the distributed computing sense as well as stability properties of the prescribed formation with the use of ideas from dynamical systems. While in the distributed computing community often only a worst-case analysis is considered, the tools of dynamical systems allow a more fine-grained analysis of the input configurations by exploring the state space. More concretely, the state space foliation describes the long-term dynamical behavior of input configurations in more detail, i.e. it allows to identify classes of configurations that converge comparably fast or slow and even classes that fail to converge to the prescribed formation. Thus, the combination of both views leads to a more profound understanding of distributed strategies for swarms of mobile robots.

Further information:

Prof. Dr. Michael Dellnitz

Chair of Applied Mathematics

Michael Dellnitz
+49 5251 60-2649
+49 5251 60-4216


Karin Senske

Chair of Applied Mathematics

Secretary Prof. Dr. Michael Dellnitz

Karin Senske
+49 5251 60-3802
+49 5251 60-3728

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