Control of spiral-wave dynamics in active media by periodic modulation of excitability

Abstract

EXCITABLE media exhibit a wide variety of geometrically complex spatio-temporal patterns, perhaps the most striking of which are rotating spiral waves. Spiral waves have now been observed in many excitable systems, including heart muscle¹, aggregating slime-mould cells², retinae³, CO oxidation on platinum⁴ and oscillatory chemical systems such as the Belousov–Zhabotinsky (BZ) reaction^5,6. In the last case, the spiral cores trace out circular or hypocycloidal trajectories, depending on the specific reaction conditions^7–9. In addition, if the excitability of the BZ reaction is light-sensitive^10–13, constant illumination has been shown to influence the dynamics of spiral waves^14,15. Here we investigate the effect of illumination that is periodically modulated in time. We find that, for a single set of reaction conditions, the motion of the spiral cores can be forced to describe a wide range of open and closed hypocycloidal trajectories, in phase with the applied modulation frequency. Numerical simulations using a modified version of the Oregonator model^16,17 of the BZ reaction reproduce this behaviour. We suggest that the modulation of excitability with weak external forces might be used as a means for controlling the dynamics of other excitable media.