Dynamical Systems
We are concerned with mathematical modeling, analysis and simulation of biological systems using methods of nonlinear dynamics. The primary focus is on microbial biofilm systems and biofilm processes. We have been studying mesoscopic models of biofilm control with antibiotics and with amensalistic or antagonistic probiotics, as well as cell-cell and inter-colony communication based on quorum sensing. Our current interest are also the upscaling from the mesoscopic to the macroscopic cell, in particular in the context of bioclogging, and chemotaxis phenomena in biofilm communities. The resulting models are usually nonlinear systems of degenerate parabolic differential equations, comprising two kind of degeneracy, that is, both porous medium and fast-diffusion, which are analysed with respect to well-posedness and longtime dynamics. This involves the study of global and expontential attractors, their fractal dimension and Kolmogorov entropy, spatio-temporal chaoticity and also trajectory attractors are investigated. The analytical work is always complemented by computer simulations.