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; the drift is assumed to be caused by a weak time-independent diffusivity gradient or convection term in the fast-variable equation. We address, to first order in the perturbation, the standard problem whose statement reads, "Given the unperturbed solution, as well as the model's parameters, predict the speed and direction of the drift in terms of the strength and direction of the perturbation." Our main results are as follows: First, we establish a mathematical equivalence between true gradients and convective perturbations; second, a variety of numerical examples, taken from computer simulations, are presented as a reference base for testing drift theories; and third, we propose a semiempirical solution to the drift problem, requiring only two quantities to be measured off the unperturbed spiral, namely, its period of rotation and the value of the fast variable at its center; good agreement with numerical simulations is found for moderately sparse spirals.