Spiral Wave Meander in Excitable Media: The Large Core Limit

We show that the dynamics of spiral waves in excitable media can be reduced to a nonlinear equation of motion for the wave tip that is asymptotically exact in a parameter range where the motion takes place around a large central core region. The onset of meander is shown to occur naturally in this range in the usual free-boundary limit where the medium exhibits an abrupt response to a stimulus. This equation provides a simple understanding of the physical origin of the meandering instability of spiral waves and of the quasiperiodic motion of the wave tip.