Spiral wave dynamics under traveling-wave modulation of excitable media

We study dynamics of spiral waves in excitable media under spatio-temporal forcing in the form of a traveling-wave modulation of a control parameter. Within a certain range of the modulation frequency a synchronized drift of a spiral wave along a straight line is obtained. A complicated cycloidal-like motion occurs outside this synchronization band. Although circulation of the spiral wave tip is in-phase with external modulation, its rotation frequency is not locked by the applied perturbation. These numerical results obtained for the Oreganator model are confirmed and complemented by analysis of a simplified kinematical model. It is shown that the observed paradoxical phase synchronization is caused by Doppler shift of the modulation frequency in a coordinate system comoving with the spiral wave core.