Control of Spiral Wave breakup by Spatiotemporal Modulation

Spiral waves are frequently observed in a large variety of excitable media, such as the Belousov– Zhabotinsky (BZ) reactions [Winfree, 1972; Ouyang & Flesselles, 1996], the catalytic surface processes [Jakubith et al., 1990], the cardiac tissue [Davidenko et al., 1992; Qu et al., 2000] and neural networks [Sbitnev, 1998]. One common feature of spiral waves is that with the variation of the environment, the dynamics of spiral waves will change dramatically. So spiral wave instability in various systems is a robust phenomenon observed in both experiments and numerical simulations [Bär & Eiswirth, 1993; Li et al., 1996; Ouyang et al., 2000; Tobia & Knobloch, 1998; Zhou & Ouyang, 2000; Sandstede & Scheel, 2000; Aranson & Kramer, 2002]. Phenomenologically, two different kinds of spiral wave breakup scenarios have been documented in experiments and numerical simulations: Doppler instability [Bär & Eiswirth, 1993; Li et al., 1996; Ouyang et al., 2000] and Eckhaus instability [Tobia & Knobloch, 1998; Zhou & Ouyang, 2000; Sandstede & Scheel, 2000; Aranson & Kramer, 2002]. The first instability usually occurs in excitable media and the spiral wave breaks up near the spiral core. In the second instability, which usually appears in oscillatory media, spiral wave breakup happens far from the spiral core, and the region near the core may remain practically unchanged. Recently, researchers find that the features and the characteristic changes of the spiral waves are of crucial importance. For instance, spiral waves in cardiac muscle can be a cause of tachycardia. Repetitious breakup of spiral waves due to Doppler instability can lead to spatiotemporal chaos, which is believed as a mechanism of ventricular fibrillation (VF). VF and sudden cardiac death are the