Two topics will covered in this talk. The first part concerns the dynamics of coupled excitable FitzHugh-Nagumo elements in the presence of noise, which is used to model the frequency variations in beating cardiac cultures. As the coupling strength increases, the frequency increases with a peak which is associated with the synchronization of the elements. The physical mechanism of frequency enhancement is due to the variation of the potential barrier for firing as the coupling changes and can be estimated by Kramer's escape rate theory which shows good agreement with simulations. The second part is about waves in phase coupled excitable medium. The corresponding phase diagrams for stable plane waves and spiral waves are obtained by simulations. This discrete model corresponds to an excitable medium with zero-refractoriness and in the continuum limit supports zero-core spiral waves.

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