title: Stability of position control of traveling waves in reaction-diffusion systems.
abstract: We consider the stability of position control of traveling waves in reaction-diffusion systems as proposed in Löber and Engel [Phys. Rev. Lett. 112, 148305 (2014)]. Instead of analyzing the controlled reaction-diffusion system, stability is studied on the reduced level of the equation of motion for the position over time of perturbed traveling waves. We find an interval of perturbations of initial conditions for which position control is stable. This interval can be interpreted as a localized region where traveling waves are susceptible to perturbations. For stationary solutions of reaction-diffusion systems with reflection symmetry, this region does not exist. Analytical results are in qualitative agreement with numerical simulations of the controlled Schlögl model.
authors.affiliation: Institut für Theoretische Physik, EW 7-1, Hardenbergstraße 36, Technische Universität Berlin, 10623 Berlin, Germany.
authors.forename: Jakob
authors.initials: J
authors.lastname: Löber
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics