Reflection and attachment of spirals at obstacles for the Fitzhugh-Nagumo and Beeler-Reuter models

In this paper, the Fitzhugh-Nagumo (FHN) equations and a modified FHN (MFHN) are considered. For the modified version, the recovery variable v has three different time scales. By considering different parameters in the local dynamics of the MFHN equations, it is observed that the phenomenon of reflection and annihilation at an impermeable boundary is observed just as in the Beeler-Reuter model. The interaction of spirals obtained with the FHN, MFHN, and Beeler-Reuter model, and an obstacle is also considered. The phenomenon of reflection of the spiral wave at a boundary changes when the boundary becomes an obstacle. Four properties for attachment of a spiral wave to an obstacle are presented in this work. © 2010 The American Physical Society.