Robustness of Biologically Inspired Pulse-Coupled Synchronization against Static Attacks

Biologically inspired pulse-coupled synchronization has received increasing attention as one of key techniques for developing decentralized wireless networks due to its inherent scalability and simplicity. While it has been actively studied in recent years, most of the previous works have focused on the synchronization only in fault/attack free networks. However, in reality, a network may have malfunctioning nodes and/or attackers, and thus robustness against these threats in the pulse- coupled synchronization must be an important practical issue on its path to realization. Motivated by this, we analyze the influence of attacker´s behaviors in a network of pulse-coupled oscillators. The analysis shows that when the number of attackers is less than a certain number, i.e. a threshold, the network sustains its synchronization. Moreover, the threshold is proportional to both of coupling strengths among the pulse-coupled oscillators and the number of legitimate oscillators. Finally, numerical experiments are given to confirm the analytic results.