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arXiv · 2605.17206

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

Till Aust·Tianfu Zhang·Andreagiovanni Reina·Heiko Hamann
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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.

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Till Aust, Tianfu Zhang, Andreagiovanni Reina, Heiko Hamann. 2026-05-17. Bimodal Synchronization Performance: Why Noise and Sparse Connectivity Can Improve Collective Timing. https://arxiv.org/abs/2605.17206

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