Hysteresis phenomenon in the dynamics of spiral waves rotating around a hole

Hysteresis in the pinning–depinning transitions of spiral waves rotating around a hole in a circular shaped two-dimensional excitable medium is studied both by use of the continuation software AUTO and by direct numerical integration of the reaction–diffusion equations for the FitzHugh–Nagumo model. In order to clarify the role of different factors in this phenomenon, a kinematical description is applied. It is found that the hysteresis phenomenon computed for the reaction–diffusion model can be reproduced qualitatively only when a nonlinear eikonal equation (i.e. velocity–curvature relationship) is assumed. However, to obtain quantitative agreement, the dispersion relation has to be taken into account.