The dynamics of spiral waves in the two-layer excitable media is studied by using the Bär-Eiswirth model. The two media adopts the inhibitory and excitatory asymmetric couplings. Numerical results show that the excitatory asymmetric coupling can promote the frequency-locking of two spiral waves with different frequencies. The two spiral waves can achieve frequency-locking even if the frequency difference between them is large. The coupling causes the two spiral waves to have the strongest ability of frequency-locking; when the coupling between the two media is the inhibitory asymmetric coupling, the two spiral waves can achieve frequency-locking only when the frequency difference of the initial spiral waves is small. Furthermore, the range of frequency-locking is smaller than that of the general feedback coupling, and the frequency-locking ability of spiral waves reaches the minimum level. When the coupling strength and control parameters are chosen appropriately, the inhibitory and excitatory asymmetric coupling can keep the spiral wave unchanged in one medium and result in the transition from spiral wave to the resting state or target wave with low-frequency in the other. The coupling also induces the meandering of spiral waves or leads to the transition from two spiral waves to two target waves in the two-layer media. Finally the generated target waves either disappear or develop into the plane-wave-like oscillation patterns. Furthermore, the oscillation of the patterns is in antiphase. In addition, the locally intermittent frequency-locking of the two spiral waves is observed. These results can help understand the complicated phenomena occurring in the cardiac system.
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