Bursting dynamics in a population of oscillatory and excitable Josephson junction

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.