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

Phase synchronization of coupled bursting neurons and the generalized Kuramoto model