Stabilization of unstable rigid rotation of spiral waves in excitable media.
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.
Schlesner
J
J
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany.
Zykov
V
V
Engel
H
H
Schöll
E
E