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

2026-05-16

AI Summary

This study investigates the mechanisms underlying the difficulty of achieving collective synchronization in pulse-coupled oscillator systems, with a focus on how stable multi-cluster states impede global synchrony. Building upon a firefly-inspired discrete-time phase model and combining phase dynamics analysis with parameter sensitivity studies, the work demonstrates that synchronization occurs only within a narrow balance window defined by specific thresholds and pulse durations. The system exhibits a bimodal behavior, alternating between highly synchronized and symmetric multi-cluster states. Notably, the research reveals that sparse connectivity and moderate noise can effectively suppress low-performance multi-cluster configurations by breaking symmetry—challenging the conventional wisdom that high connectivity and noise-free conditions are optimal. The study further delineates the critical parameter regimes necessary for robust and efficient synchronization.

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.

Problem

• bimodal synchronization
• pulse-coupled oscillators
• multi-cluster states
• collective timing
• quorum threshold

Innovation

• pulse-coupled oscillators
• bimodal synchronization
• quorum threshold
• sparse connectivity
• noise-induced synchronization