  Bursting neurons fire rapid sequences of action potential spikes followed by
a quiescent period. The basic dynamical mechanism of bursting is the slow
currents that modulate a fast spiking activity caused by rapid ionic currents.
Minimal models of bursting neurons must include both effects. We considered one
of these models and its relation with a generalized Kuramoto model, thanks to
the definition of a geometrical phase for bursting and a corresponding
frequency. We considered neuronal networks with different connection topologies
and investigated the transition from a non-synchronized to a partially
phase-synchronized state as the coupling strength is varied. The numerically
determined critical coupling strength value for this transition to occur is
compared with theoretical results valid for the generalized Kuramoto model.
