A quantitative theory for phase-locking of meandering spiral waves in a rotating external field

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.