Bimodal Synchronization Performance: Why Noise and Sparse Connectivity Can Improve Collective Timing
For designers of decentralized time coordination systems, this work challenges the assumption that high connectivity and low noise are optimal, offering a counterintuitive design principle.
The paper analyzes a firefly-inspired synchronization model and finds that collective synchrony emerges only near a critical balance between quorum threshold and pulse duration. It shows that reducing connectivity or introducing noise can suppress low-performance multi-cluster states, improving overall synchronization.
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.