  We consider networks of weakly pulse-coupled identical oscillators. In an
effort to resolve a long-standing problem, we develop an analytic condition on
the infinitesimal phase response curve (iPRC) for synchronized dynamic
behaviour, extending the well-known result by Mirollo and Strogatz. Oscillators
cluster towards synchronization through recurrent absorptions in the case of
fully connected networks. We also point out that the same analytic condition
guarantees absorption for general networks, and how the condition is extended
for non-homogeneous coupling. For a network of neural oscillators of the
quadratic-integrate-and-fire type (QIF) we reinterpret our synchronization
result into explicit conditions on the QIF-model parameters.
