Dresden 2014 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 35: Reaction-Diffusion Systems

DY 35.1: Talk

Thursday, April 3, 2014, 15:00–15:15, HÜL 186

Position and shape control of traveling waves in reaction-diffusion systems — Jakob Löber, •Steffen Martens, and Harald Engel — Technische Universität, Berlin, Deutschland

We present an efficient and easily applicable method to control the position respectively the shape of traveling wave solutions in reaction-diffusion systems according to a desired protocol of movement. Given this protocol, the control function is found as the solution of a perturbatively derived integral equation. In particular, we derived an analytical expression for the space (r) and time (t) dependent control function f(r,t) that is valid for a large variety of reaction-diffusion systems and many kinds of protocols, e.g., accelerating, decelerating or periodic protocols. Intriguingly, our control method is expressed in terms of the uncontrolled wave profile and its propagation velocity, rendering detailed informations about the reaction kinetics unnecessary. Noteworthy, this method is very close to optimal controls. An extension of the control method allows to control the shape of traveling fronts as well as localized spots in two and three spatial dimensions.