  Transient dynamics leading to the synchrony of pulse-coupled oscillators has
previously been studied as an aggregation process of synchronous clusters, and
a rate equation for the cluster size distribution has been proposed. However,
the evolution of the cluster size distribution for general cluster sizes has
not been solved yet. In this paper, we study the evolution of the cluster size
distribution from the perspective of a percolation model by regarding the
number of aggregations as the number of attached bonds. Specifically, we derive
the scaling form of the cluster size distribution with specific values of the
critical exponents using the property that the characteristic cluster size
diverges as the percolation threshold is approached from below. Through
simulation, it is confirmed that the scaling form well explains the evolution
of the cluster size distribution. Based on the distribution behavior, we find
that a giant cluster of all oscillators is formed discontinuously at the
threshold and also that further aggregation does not occur like in a
one-dimensional bond percolation model. Finally, we discuss the origin of the
discontinuous formation of the giant cluster from the perspective of global
suppression in explosive percolation models. For this, we approximate the
aggregation process as a cluster--cluster aggregation with a given collision
kernel. We believe that the theoretical approach presented in this paper can be
used to understand the transient dynamics of a broad range of synchronizations.
