  In this work we revisit the nonmonotonic behavior (NMB) of synchronization
time with velocity reported for systems of mobile pulse-coupled oscillators
(PCOs). We devise a control parameter that allows us to predict in which range
of velocities NMB may occur, also uncovering the conditions allowing us to
establish the emergence of NMB based on specific features of the connectivity
rule. Specifically, our results show that if the connectivity rule is such that
the interaction patterns are sparse and, more importantly, include a large
fraction of non reciprocal interactions, then the system will display NMB. We
furthermore provide a microscopic explanation relating the presence of such
features of the connectivity patterns to the existence of local clusters unable
to synchronize, termed frustrated clusters, for which we also give a precise
definition in terms of simple graph concepts. We conclude that, if the
probability of finding a frustrated cluster in a system of moving PCOs is high
enough, NMB occurs in a predictable range of velocities.
