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A discontinuous map of a slow control variable is constructed in this paper.It captures essential features of the period-adding bifurcation scenarios observed in both experiment and simulations with differential Chay model.A particularly designed experiment shows typical bifurcations from period 1 to period 5 with stochastic bursting patterns in a neuronal pacemaker.These stochastic bursting patterns are reproduced and explained by the constructed discontinuous map added with white noise.The numeric calculation shows that the discontinuous map can well approximate the basic structure of the first return map formed by ISI series of the periodic bursting.