Localized sensitivity of spiral waves in the complex Ginzburg-Landau equation

Dynamics of spiral waves in perturbed (e.g., slightly inhomogeneous) two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. These forces are defined as convolutions of the perturbation with the so-called response functions. In this paper, we find the response functions numerically for the spiral waves in the complex Ginzburg-Landau equation, and show that they exponentially decrease with distance.