Pulse-coupled oscillator models inspired by firefly synchronization are widely used to study decentralized time coordination in distributed systems. We analyze a discrete-time, discrete-phase firefly-inspired synchronization model and show that collective synchrony emerges only near a critical balance between the quorum threshold (fraction of pulsing neighbors required to trigger a phase update) and the pulse duration (how long agents remain detectable to others). Within this parameter region, the system exhibits bimodal performance: it either reaches near-perfect synchronization or becomes trapped in stable multi-cluster states, where symmetrically phase-offset subgroups mutually reinforce one another and prevent global synchrony. Our analysis shows that reducing connectivity or introducing noise suppresses these low-performance states by breaking such symmetric interactions, indicating that highly connected or noiseless systems are not necessarily optimal for collective synchronization.

翻译：受萤火虫同步启发的脉冲耦合振荡器模型被广泛用于研究分布式系统中的分散式时间协调。我们分析了一个离散时间、离散相位的萤火虫启发同步模型，并证明集体同步仅在法定阈值（触发相位更新所需相邻脉冲节点的比例）与脉冲持续时间（代理节点保持可被其他节点检测的时间）之间的临界平衡区域内出现。在此参数区域内，系统呈现出双峰性能：要么达到近乎完美的同步，要么陷入稳定的多簇状态——其中对称相位偏移的子群相互强化，阻碍全局同步。我们的分析表明，降低连接性或引入噪声可通过打破这种对称相互作用来抑制低性能状态，这意味着高连接或无噪声系统并非总能为集体同步提供最优条件。