Parametric forcing of scroll-wave patterns in three-dimensional excitable media

The dynamics of axisymmetric and twisted scroll rings under homogeneous periodic forcing is studied numerically. The collapse of axisymmetric rings can be enhanced or retarded significantly with resonant forcing. Twisted scroll rings exhibit the phenomenon of resonant drift in a direction normal to the axis of the central filament. The scaling of mean and fluctuating axial drift due to forcing is determined. Evidence is provided showing that the appropriate symmetry group for the dynamics of the unforced twisted scroll ring is SE(2)×R. Ordinary differential equations based on symmetry considerations explain the dynamics without resorting to laws of filament motion and the local geometry hypothesis.