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. (C) 2009 Elsevier B.V. All rights reserved.