@article{ZykovBordyugovLentzetal.2010,
  author    = {Zykov, Vladimir and Bordyugov, Grigory and Lentz, Hartmut and Engel, Harald},
  title     = {Hysteresis phenomenon in the dynamics of spiral waves rotating around a hole},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2009.07.018},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}