Re-entrant cardiac arrhythmias can be idealized as spiral wave or scroll wave solutions of reaction-diffusion equations of excitable media, see Holden, Markus and Othmer [17]; Panfilov and Holden [21]. The elimination of such arrhythmias, or the defibrillation of heart muscle, is a vitally important problem, as re-entrant activity in ventricular muscle can be lethal. Biktashev and Holden [5]-[7], Biktashev [4] have proposed exploiting resonant drift of spiral wave position, produced by low amplitude forcing under feedback control (to overcome effects of boundaries and inhomogeneities) to defibrillate cardiac tissue by gently pushing out re-entrant sources. The feasibility of this approach has been illustrated by numerical computations within Cartesian coordinates, using biophysically derived excitation equations for mammalian atrial and ventricular tissue, Biktashev and Holden [8], [9].
The heart has a complicated, anisotropic and moving geometry [17], and as a step to modelling the endocardial surface of the atrium as a spherical surface we examine induced resonant drift of rigidly rotating spiral waves in circular and annular domains. A circular domain also provides a natural model for experiments on chemical excitable media in a thin film in a Petri dish e.g., see Grill et al [16], Müller et al [20], and Gómez-Gesteira et al [15].