Computational analysis of structure formation processes
This project is part the research center "Mathematisierung"
within this program PhD theses are supervised, which cover the whole process of mathematical modeling:
from the natural system (of biological, chemical or pysical origin) through the
different steps of simplification to a mathematical formulation and from the development of new mathematical theories to their numerical realisation. The main focus is on the development of numerical methods for the computation of structure formation phenomena.
The essential idea is to compute the limit sets (stationary states, periodic and homoclinic solutions and strange attractors) directly from boundary value problems. For complex long time behaviour this implies the computation of invariant measures.
Within this broad scope the following special problems are treated:
- Computation of spiral waves and their bifurcations in reaction-diffusion equations,
- invariant measures and phase transitions in dynamical systems on lattices
(in cooperation with Ph. Blanchard),
- neuronal control of simple biomechanical systems (in cooperation with H. Ritter).