Effect of delay on the synchronization of weakly coupled neurons via excitatory chemical synapses

Excitatory chemical coupling connections are ubiquitous in neuronal system. In this paper, we investigate the effect of conduction time delays on synchronization properties of weakly coupled Morris-Lecar neuronal oscillators via excitatory chemical synapses. We first reduce the complex neuronal dynamics to a simple phase model by means of phase-model reduction method. Then we examine the roles of time delays extensively on the synchronization properties by bifurcation analysis and numerical simulation. Finally, we identify the existence and the stability of various phase-locked states, including in-phase, anti-phase and out-of-phase synchronization states.