  We investigate the collective dynamics of bursting neurons on clustered
network. The clustered network is composed of subnetworks each presenting a
small-world property, and in a given subnetwork each neuron has a probability
to be connected to the other subnetworks. We give bounds for the critical
coupling strength to obtain global burst synchronization in terms of the
network structure, i.e., intracluster and intercluster probabilities
connections. As the heterogeneity in the network is reduced the network global
synchronization is improved. We show that the transitions to global synchrony
may be abrupt or smooth depending on the intercluster probability.
