The isolated beating cells have different intrinsic excitatory period interval with fluctuation. The excitatory conduction between the beating cells synchronizes with time when such beating cells formed a cellular clot, which eventually shows single excitatory period interval. However, as of yet, it is not clear how the beating cell regulates the excitatory action of other cells. On the other hand, FitzHugh, Nagumo et al. and Hodgkin et al. proposed a kinetic mathematical model which made it possible to realize the excitatory action numerically. The numerical simulation makes it possible to analyze several effects of the excitatory period interval on the synchronization based on the experimentally observed data, so it is useful for elucidation of a mechanism of the synchronization. In the current study, with employing a kinetic mathematical model for the excitatory conduction, we developed a novel numerical simulator for which excitatory wave propagates on a two-dimensional cellular matrix, and numerically analyzed an interference of excitatory conduction. In addition, we verified several effects of both average and fluctuation for the excitatory period interval on the synchronization of excitatory conduction. Our proposed numerical simulator constructed by employing Barkley's model qualitatively realized a synchronization of excitatory conduction between beating cells. The synchronization of excitatory conduction was regulated by single cell for which both the average and standard deviation for excitatory period interval is smaller than those of other cells. As a result, it was clear that both the average and the standard deviation for the excitatory period interval played an important role in the synchronization of excitatory conduction between beating cells. Therefore, a consideration of both the average and the standard deviation for excitatory period interval is indispensable to elucidation of a mechanism of the synchronization between beating cells.