  We report parabolic bursting in a globally coupled network of mixed
population of oscillatory and excitable Josephson junctions. The
resistive-capacitive shunted junction (RCSJ) model of the superconducitng
device is used for this study. We focus on the parameter regime of the junction
where its dynamics is governed by the saddle-node on invariant circle (SNIC)
bifurcation. In this SNIC regime, the bursting appears in a broad paramater
space of the ensemble of mixed junctions. For a coupling value above a
threshold, the network splits into two synchronized clusters when a
reductionism approach is applied to reproduce the bursting behavior of the
large network. The excitable junctions effectively induces a slow dynamics in
the network to generate bursting. This bursting is a generic property of a
globally coupled network with a mixed population of dynamical nodes where each
node posseses the SNIC property.
