Abstract
Inhibitory chemical coupling connections are ubiquitous in neuronal system. In this paper, 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. Along with the expected phase and anti-phase synchronization regimes, we find the emergent phenomena that significantly influence the synchronization behavior.
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