title: Stabilization of unstable rigid rotation of spiral waves in excitable media.
abstract: Depending on the parameters of two-dimensional excitable or oscillatory media rigidly rotating or meandering spiral waves are observed. The transition from rigid rotation to meandering motion occurs via a supercritical Hopf bifurcation. To stabilize rigid rotation in a parameter range beyond the Hopf bifurcation, we propose and successfully apply a proportional control algorithm as well as time delay autosynchronization. Both control methods are noninvasive. This allows for determination of the parameters of unstable rigid rotation of spiral waves either for a model or an experimental system. Using the Oregonator model for the light-sensitive Belousov-Zhabotinsky reaction as a representative example we show that quite naturally some latency time appears in the control loop, and propose an efficient method to overcome its destabilizing influence.
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany.
authors.forename: J
authors.initials: J
authors.lastname: Schlesner
authors.forename: V
authors.initials: V
authors.lastname: Zykov
authors.forename: H
authors.initials: H
authors.lastname: Engel
authors.forename: E
authors.initials: E
authors.lastname: Schöll