Bimodal Synchronization Performance: Why Noise and Sparse Connectivity Can Improve Collective Timing

TL;DR

This paper investigates how noise and sparse connectivity can enhance collective timing in firefly-inspired synchronization models by analyzing the emergence of synchrony and multi-cluster states near a critical parameter balance.

Contribution

It reveals that optimal synchronization occurs near a critical quorum threshold and pulse duration, and that noise and reduced connectivity can improve performance by disrupting stable multi-cluster states.

Findings

Synchronization emerges near a critical parameter balance.

Noise and sparse connectivity suppress multi-cluster states.

Highly connected or noiseless systems are not always optimal.

Abstract

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.