  We develop a formalism to analyze the behaviour of pulse--coupled identical
phase oscillators with a specific attention devoted to the onset of partial
synchronization. The method, which allows describing the dynamics both at the
microscopic and macroscopic level, is introduced in a general context, but then
the application to the dynamics of leaky integrate-and-fire (LIF) neurons is
analysed. As a result, we derive a set of delayed equations describing exactly
the LIF behaviour in the thermodynamic limit. We also investigate the weak
coupling regime by means of a perturbative analysis, which reveals that the
evolution rule reduces to a set of ordinary differential equations. Robustness
and generality of the partial synchronization regime is finally tested both by
adding noise and considering different force fields.
