Phase synchronization of a pair of spiral waves

The interaction of a pair of spiral waves with different independent rotation frequencies is studied. In a very large frequency mismatch searching region, we observe three different pattern formation phenomena: (a) phase-synchronization-induced invasion under a relatively small frequency mismatch, i.e., the spiral wave with slower frequency (longer period) is swept away by a traveling wave, which is induced and phase synchronized by the faster spiral wave; (b) the coexistence of two spiral waves at sufficiently large parameter mismatch; and (c) an intermediate state, a non-phase-synchronous invasion, that is, similarly the slower spiral wave is swept by an approximate planar wave, whose frequency, however, is intermediate between those of the faster and slower waves. A point-source model is studied to analyze all these phenomena in a unified way.