Abstract
•Spiral waves are fascinating, visually appealing, and important phenomena in excitable media.•We study two-layer excitable media where spiral wave turbulence is triggered initially.•The effects of periodic plane waves on the dynamics of spiral wave turbulence are studied.•Low spatial frequency waves are unable to eliminate spiral wave turbulence.•Plane waves with sufficiently high spatial frequency successfully terminate turbulence.
Spiral waves are relatively common, yet fascinating, visually appealing, and important phenomena in many nonlinear dynamical systems. The emergence of spiral waves in the heart’s atrium, for example, signals abnormality that can lead to arrhythmias such as atrial flutter and atrial fibrillation. Spiral waves have also been associated with the disruption of resting states in the human brain, which are crucial for unimpaired cognitive ability and information processing. Here we consider two-layer excitable media, where spiral wave turbulence is triggered as the initial state. We study the effects of periodic plane waves on the dynamics of spiral wave turbulence, in particular by varying their spatial frequency. Our research shows that planes waves with low spatial frequency are in general too weak to overcome spiral wave turbulence. But when the spatial frequency is sufficiently increased, the plane waves can overcome spiral wave turbulence and impose a stripped spatial pattern over the excitable media. By increasing the spatial frequency of the plane waves even further, we show that it is possible to minimize the time needed to destroy spiral wave turbulence, although we also observe an upper limit beyond which the recurrence of turbulence is likely. This is linked to residual spirals that remain following a too rash elimination attempt, which then gradually regain footing across the whole medium.