Research on time synchronization of linear pulse-coupled oscillators model with delay in nearest neighbor wireless multi-hop networks

Time synchronicity works as a popular requirement in wireless sensor networks. Pulse-coupled oscillators similar to firefly flashing and synchronization via discrete pulse coupling are widely used in wireless sensor networks. In this article, we have studied the time synchronization with communication delay in the nearest neighbor network of distributed sensors, based on the pulse-coupled oscillators model of synchronicity achieved by biological systems. First, we present a linear pulse-coupled oscillators model with coupling delay and the model is used to analyze the wireless sensor networks synchronization with communication delay. Second, we mathematically analyze the firing behaviors in the linear pulse-coupled oscillators network using the delayed excitatory coupling and track the synchronization process of the two and multi-oscillators and obtain the synchronization conditions from the regression mapping. Finally, through the proposed model implementation in the wireless sensor networks simulation framework, we demonstrate that the multi-oscillators system can be synchronized from a random starting stage distribution under linear phase responding functions and the nearest neighbor communication. The results show that our approach can achieve clock synchronization in wireless sensor networks with delayed nearest neighbor communication.