Sharp versus smooth synchronization transition of locally coupled oscillators

We provide a general condition for the occurrence of a sudden transition to synchronization in an array of oscillators mutually coupled via the nearest neighbors. At the onset of synchronization a specific constraint must be fulfilled, precisely, the response time of a single system to signals from the adjacent sites must be smaller than the refractory period. We verify this criterion in some models for neuronal dynamics, namely, in excitable systems driven by noise as well as in chaotic oscillators.