B6: Control of travelling and rotating waves in spatially extended nonlinear systems

Principal investigators:

Prof. Dr. Harald Engel [1]
Prof. Dr. Fredi Tröltzsch [2]

Project summary:

We aim at controlling self-organized spatio-temporal patterns in active media. In particular, we guide non-linear waves and moving localized spots according to a given protocol of movement within two- and three- dimensional domains. To reach our control goals we apply methods based on multiple scale perturbation theory for position and shape control and exploit the powerful methods of optimal control of partial differential equations including sparse control and pointwise state constraints. Additionally, we investigate the impact of spatial confinement on wave and spot dynamics and study reaction-diffusion processes in small compartments.