Nonidentical Linear Pulse-Coupled Oscillators Model With Application to Time Synchronization in Wireless Sensor Networks

Similar to other cyber infrastructure systems, as wireless sensor networks become larger and more complex, many classic algorithms may no longer work efficiently. This paper presents a wireless sensor network time synchronization model that was initially inspired by synchronous flashing of fireflies. Synchronous flashing of fireflies is an interesting phenomenon that has been studied for decades. A variety of models have been proposed to explain this phenomenon, among which is the pulse-coupled oscillators model that models fireflies as oscillators. The oscillators in such a model interact only through discrete pulses, similar to the flashing of fireflies. In this paper, we propose a new nonidentical linear pulse-coupled oscillators model and use the model to analyze synchronization of pulse-coupled oscillators with different frequencies. The conditions to achieve and maintain synchronization are derived, and then, the results are used to prove that the oscillators in the model can achieve synchronization eventually, except for a set of frequencies with zero Lebesgue measure. Furthermore, through simulations and implementation on a wireless sensor network testbed, we demonstrate that the proposed nonidentical linear pulse-coupled oscillators model can be used in designing lightweight scalable time synchronization protocols for distributed systems.