In this paper, an artificial sub-threshold oscillating spiking neuron is presented and its response phenomena to an input spike-train are analyzed. In addition, a dynamic parameter update rule of the neuron for achieving synchronizations to the input spike-train having various spike frequencies is presented. Using an analytical two-dimensional return map, local stability of the parameter update rule is analyzed. Furthermore, a pulse-coupled network of the neurons is presented and its basic self-organizing function is analyzed. Fundamental comparisons are also presented.