Effect of excitability on partially pinned scroll waves in excitable chemical media.

Abstract

We present an investigation of excitability effects on the dynamics of scroll waves partially pinned to inert cylindrical obstacles in three-dimensional Belousov-Zhabotinsky excitable media. We also report on corresponding numerical simulations with the Oregonator model. The excitability varies according to the concentration of sulfuric acid [H_{2}SO_{4}] in the Belousov-Zhabotinsky (BZ) reaction and the parameter ɛ^{-1} in the Oregonator model. Initially, the freely rotating scroll segment rotates faster than the pinned one. The difference in the frequency of the two parts results in a transition from a straight pinned scroll wave to a twisted one, which helically wraps around the entire obstacle. The wave frequency in the whole volume is equal to that of the freely rotating scroll wave. When the excitability is increased, the time for the transition to the twisted wave structure decreases while the average speed s of the development increases. After the transition, the twisted wave remains stable. In media with higher excitability, the helical pitch is shorter but the twist rate ω is higher. Analysis presented in this study together with our previous findings of the effect of the cylindrical obstacle diameter on the wave dynamics results in common features: The average speed s and the twist rate ω of both studies fit well to functions of the difference in the initial frequency Δf of the freely rotating and untwisted pinned waves. We also demonstrate the robustness of the partially pinned scroll waves against perturbations from spontaneous waves emerging during the wave generation in the BZ medium with high [H_{2}SO_{4}]. Even though the scroll wave is partly disturbed at the beginning of the experiment, the spontaneous waves are gradually suppressed and the typical wave structure is finally developed.