Building phase synchronization equivalence between coupled bursting neurons and phase oscillators

Bursting neurons are characterized by an alternation of active and inactive state, during the active state they exhibit train of spikes and quiescent behavior in the inactive state. When bursting neurons are coupled they can synchronize depending on the coupling strength. If the coupling strength is increased above a critical value, a transition from an asynchronous state to a partial synchronized state can be observed. This transition has the same type observed in coupled Kuramoto oscillators. When the natural frequency distribution of the oscillators is properly defined, the bursting neurons and the Kuramoto oscillators describe the same phase transition for synchronization.