We present master-slave pulse-coupled bifurcating neurons having refractoriness. The system can exhibit various phenomena, e. g. , periodic and chaotic in-phase synchronizations, and periodic out-of-phase synchronization. We clarify local stabilities of the phenomena and a sufficient condition for the in-phase synchronization. It is suggested that bifurcations of the synchronization phenomena may relate to detection of a master parameter, and the refractoriness may relate to control of the detection accuracy. Using a simple test circuit, typical phenomena are verified in the laboratory.