  Characteristic versus critical features of earthquakes are studied on the
basis of the Olami-Feder-Christensen model. It is found that the local
recurrence-time distribution exhibits a sharp $\delta$-function-like peak
corresponding to rhythmic recurrence of events with a fixed ``period'' uniquely
determined by the transmission parameter of the model, together with a
power-law-like tail corresponding to scale-free recurrence of events. The model
exhibits phenomena closely resembling the asperity known in seismology.
