  We study the occurrence of cuspy events on a light string stretched between
two Y-junctions with fixed heavy strings. We first present an analytic study
and give a solid criterion to discriminate between cuspy and non-cuspy string
configurations. We then describe a numerical code, built to test this analysis.
Our numerical investigation allows us to look at the correlations between
string network's parameters and the occurrence of cuspy phenomena. We show that
the presence of large amplitude waves on the light string leads to cuspy
events. We then relate the occurrence of cuspy events to features like the
number of vibration modes on the string or the string's root-mean-square
velocity.
