This paper presents the synchronization of a population of identical moving pulse-coupled oscillators (MPCOs) that are confined to move in a plane with mutual interactions, which are controlled by some pre-determined state threshold values and only take effect inside some known communication radii. The states are allowed to evolve in a nonlinear and periodical manner in accordance with a smooth, monotonically increasing and concave down function. Sufficient conditions are established for synchronization and the general effects of system parameters on the synchronization rate are further probed into. It is found that increasing signal strength causes the synchronization rate to initially decrease, then remain almost constant, then increase again until it finally decreases. Furthermore, with increasing speed modulus the synchronization rate initially decreases then increases. The synchronization rate, however, decreases with an increasing communication radius. Finally, as a real-world application, the proposed model is used to synchronize the different clocks in an ultra-wide bandwidth wireless ad hoc network.