Linear stability analysis of rotating spiral waves in excitable media

Abstract

Fast numerical methods are used to solve the equations for periodically rotating spiral waves in excitable media, and the associated eigenvalue problem for the stability of these waves. Both equally and singly diffusive media are treated. Rotating-wave solutions are found to be discretely selected by the system and an isolated, complex-conjugate pair of eigenmodes is shown to cause instability of these waves. The instability arises at the point of zero curvature on the spiral interface and results in wavelike disturbances which propagate from this point along the interface.