Spiral drift and core properties

We consider the drift of a stable, nonmeandering rotating spiral wave in a singly diffusive FitzHugh-Nagumo medium with generic reaction functions; th e drift is assumed to be caused by a weak time-independent diffusivity grad ient or convection term in the fast-variable equation. We address, to first order in the perturbation, the standard problem whose statement reads, "Gi ven the unperturbed solution, as well as thr model's parameters, predict th e speed and direction of the drift in terms of the strength and direction o f the perturbation." Our main results are as follows: First, we establish a mathematical equivalence between true gradients and convective perturbatio ns; second, a variety of numerical examples, taken from computer simulation s, are presented as a reference base for testing drift theories; and third, we propose a semiempirical solution to the drift problem, requiring only t wo quantities to be measured off the unperturbed spiral, namely, its period of rotation and the value of the fast variable at its center; good agreeme nt with numerical simulations is found for moderately sparse spirals. [S106 3-651X(99)16705-9].