Feedback resonant drift monitored by wavetip orientation

An ideal way to avoid the resonant repulsion from the boundaries is to monitor the instantaneous frequencies of the rotation of the wave tip, as described in Sect.2.6, and thereby to apply the resonant forcing at exactly the same phase of resonantly drifting spiral each rotation [7]. Figure 3 illustrates the spiral wave response to a spatially uniform perturbation applied at the same phases of the rotating wave. In 3(a) the amplitude of the perturbation is insufficient to overcome the non-resonant interaction with the boundary, and the counter-clockwise rotating spiral drifts clockwise around the boundary, slowing down and finally freezing in position with its tip's trajectory approaching a cycle that does not move, where the effects of resonant forcing and the interaction with the boundary cancel each other. In 3(b) the amplitude of the perturbation is larger, the linear drift velocity is larger, and the spiral collides and is extinguished at the boundary. In 3(c) and (d) interactions with an interior obstacle, an inexcitable hole, are illustrated; in (c) the spiral is trapped around a small hole (whose diameter is less than the core diameter) and finally breaks free, and is extinguished at the boundary, while in 3(d) the spiral is trapped and bound by a hole that has a diameter larger than the spiral core diameter.

  
Figure 3: Feedback resonant drift produced by spatially uniform, repetitive stimulation controlled by monitoring the wavetip orientation. Amplitude of perturbation A = 2.5 in (a), and A=3 in (b)-(d). The * marks the position of the wave's tip at which the perturbation is applied. (a) Stimulation amplitude is not large enough to extinguish the resonantly drifting spiral wave, and the core moves around the boundary, and is finally frozen at the boundary. (b) Resonantly drifting spiral wave is extinguished at the boundary by the higher amplitude stimulation. (c) Resonantly drifting spiral wave attaches to, and is detached from, a small hole with radius , and finally collides with, and is extinguished at, the boundary. (d) Resonantly drifting spiral wave becomes attached and bound to a hole with radius .