A4: Spatio-temporal patterns: control, delays, and design

Principal investigators:

Prof. Dr. Bernold Fiedler

Dr. Isabelle Schneider


Project summary:

Spatio-temporal patterns encompass a plethora of phenomena in Sciences and Engineering. Their mathematical understanding is comparably limited, mostly to patterns in partial differential equations ofreaction-diffusion type, and to ordinary differential equations on very regular, symmetric, or small networks. In marked contrast to more traditional lines of research, our goal is a qualitative approach toopen loop and feedback control, including networks and beneficial delays, and ultimately the rational design of spatial and temporal patterns of applied relevance. We therefore address three areas: delayed feedback control, qualitative analysis of networks, and design and control of global dynamics.