  The role of intermediaries in the synchronization of small groups of light
controlled oscillators (LCO) is addressed. A single LCO is a two-time-scale
phase oscillator. When pulse-coupling two LCOs, the synchronization time
decreases monotonously as the coupling strength increases, independent of the
initial conditions and frequency detuning. In this work we study numerically
the effects that a third LCO induces to the collective behavior of the system.
We analyze the new system by dealing with directed heterogeneous couplings
among the units. We report a novel and robust phenomenon, absent when coupling
two LCOs, which consists of a discontinuous relationship between the
synchronization time and coupling strength or initial conditions. The mechanism
responsible for the appearance of such discontinuities is discussed.
