Synchronization of pulse-coupled oscillators (PCOs) has gained significant attention recently due to their increased applications in sensor networks and wireless communications. Given the distributed and unattended nature of wireless sensor networks, it is imperative to enhance the resilience of PCO synchronization against malicious attacks. However, most existing results on attack-resilient pulse-based synchronization are obtained under assumptions of all-to-all coupling topologies or restricted initial phase distributions. In this paper, we propose a new pulse-based synchronization mechanism to improve the attack resilience of PCO synchronization that is applicable to non-all-to-all networks. Under the proposed synchronization mechanism, we prove that perfect synchronization of legitimate oscillators can be guaranteed in the presence of multiple Byzantine attackers who can emit attack pulses arbitrarily without any constraint except that practical bit rate constraint renders the number of pulses from an attacker to be finite. The new mechanism can guarantee synchronization even when the initial phases of all legitimate oscillators are arbitrarily distributed in the entire oscillation period, which is in distinct difference from most existing attack-resilient synchronization approaches (including the seminal paper from Lamport and Melliar-Smith [1]) that require a priori (almost) synchronization among legitimate oscillators. Numerical simulation results are given to confirm the theoretical results.

中文翻译：

---

拜占庭攻击下脉冲耦合振荡器网络的全局同步

脉冲耦合振荡器 (PCO) 的同步最近因其在传感器网络和无线通信中的应用增加而受到广泛关注。鉴于无线传感器网络的分布式和无人值守特性，必须增强 PCO 同步对抗恶意攻击的弹性。然而，大多数现有的基于脉冲的抗攻击同步结果是在全对全耦合拓扑或受限初始相位分布的假设下获得的。在本文中，我们提出了一种新的基于脉冲的同步机制，以提高适用于非全对全网络的 PCO 同步的攻击弹性。在建议的同步机制下，我们证明了在多个拜占庭攻击者存在的情况下可以保证合法振荡器的完美同步，这些攻击者可以不受任何限制地任意发射攻击脉冲，但实际的比特率限制使得来自攻击者的脉冲数量是有限的。即使所有合法振荡器的初始相位在整个振荡周期内任意分布，新机制也可以保证同步，这与大多数现有的抗攻击同步方法（包括来自 Lamport 和 Melliar-Smith 的开创性论文 [1 ]) 需要合法振荡器之间的先验（几乎）同步。给出了数值模拟结果以证实理论结果。