Abstract
It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris–Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.