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.