Response functions of spiral waves in the FitzHugh-Nagumo system

Spiral waves are rotating solutions of nonlinear reaction-diffusion systems in two spatial dimensions. Due to the symmetries of the plane, a spiral wave can be shifted and rotated arbitrary, still remaining a solution to reaction-diffusion system. Introducing a symmetry-breaking perturbation of the reaction-diffusion equation, the spiral wave begins to drift, i.e. change its rotation phase and its position on the plane. On the linear level (for small perturbations), the velocity of drift can be calculated using the perturbation technique, projecting on the symmetry subspaces of the unperturbed equation. For the projection one needs the eigenfunctions of the adjoint problem, since the linearization of reaction-diffusion problem is not self-adjoint. Those adjoint eigenfunctions are called response functions of spiral waves. In this paper, I will present results of computations of response functions and compare the predictions of drift velocities with the help of those with the direct numerical simulations of drifting spirals in reaction-diffusion system. Both results turn out to be in a nearly perfect quantitative agreement.