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We present a novel hybrid spiking neuron that is a wired system of shift registers and behaves like an analog spiking neuron model. The presented neuron exhibits various bifurcation phenomena and response characteristics to an input spike train. We derive continuous discrete hybrid maps that can describe the neuron dynamics analytically. By using these maps, the typical mechanisms of bifurcations and responses are clarified. We also present a novel field-programmable gate-array-friendly online learning algorithm for the neuron. It is shown that the algorithm enables the neuron to reconstruct the response characteristics of another neuron with unknown parameter values. Typical learning functions are also validated by experimental measurements.