Synchronization of coupled fast-spiking neurons with chemical synapses is studied in this paper. It is shown that by varying some key parameters such as the coupling strength and the decay rate of synapses, two coupled fast-spiking neurons can exhibit various firing synchronizations including periodic and chaotic motions. Different types of firing synchronizations are diagnosed by means of bifurcation diagrams and the largest Lyapunov exponent of the error dynamical system. However, with the synaptic delay considered, two coupled neurons can show different types of transitions of in-phase and anti-phase synchronizations and these transitions can be identified from the bifurcation diagrams and the variations of the phase errors of the coupled neurons. The revealed complicated synchronization modes effectively provide important guidelines to understanding collective behaviors of coupled neurons.
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