Abstract
When a rotating external field larger than a critical strength is applied to a meandering spiral with frequency close to the spiral frequency, the spiral may phase-lock to the applied field and perform rigid rotation instead. We show that this conversion happens by stabilization of an unstable circular-core spiral due to the external field. From calculating overlap integrals of adjoint critical modes (response functions), the Arnold tongue for phase-locking is predicted, matching the outcome from direct numerical simulations.
Highlights
Rotating spiral waves are among the most fascinating examples of self-organizing spatiotemporal patterns that have been observed in diverse systems outside of equilibrium [1, 2]
Our present aim is to provide a quantitative theory and to elucidate the mechanism behind the phenomenon of stabilization of meandering spiral waves and synchronous motion of the tip along with the applied rotating electric field. (See our numerical results in figure 1 where we show the initial meandering spiral wave, the phase-locked spiral and the Arnold tongue for phaselocking (PL).) in the present work we for the first time provide a theoretical prediction of the asymmetric Arnold tongue region for the stable phase-locked spiral waves, which matches the outcome from direct simulations very well
In the Barkley model that we presently investigate, the flower-like tip trajectory of the spiral indicates that the system is still close to the Hopf bifurcation, e.g. in contrast ionic cardiac models which have meander due to a dynamical wave block
Summary
Rotating spiral waves are among the most fascinating examples of self-organizing spatiotemporal patterns that have been observed in diverse systems outside of equilibrium [1, 2]. The dynamics of a spiral wave is often characterized and to some extent even determined by the motion of the tip [14, 15]. Quasi-periodic motions of the spiral tip are possible and this phenomenon was called ‘meander’ [16,17,18]. Such meandering of spiral waves has been experimentally observed, e.g. in BZ systems [19, 20] as well as in cardiac tissue [21]. Meander occurs generally in two types called outward meandering and inward meandering, dependent of whether their tip trajectory forms a flower-like orbit with petals pointing outward or inward
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