The dynamics of spiral waves in a pair of linearly coupled reaction-diffusion systems is investigated. We find that the spiral dynamics depends on the coupling strength between the two subsystems. When the coupling strength is weak, the frequency and wavelength of the spiral wave in each subsystem remain unchanged. The interaction between the two subsystems induces the drift of spiral waves. When the coupling strength is strong, synchronization between the two subsystems is established. The two subsystems play different roles in the collective dynamics: one subsystem is always dominant and enslaves the other.
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