Pulse-coupled oscillator synchronization: Bridging theory and experiments with electronic firefly networks

While continuous coupled oscillator models, such as the Kuramoto model, have been extensively investigated, a comprehensive framework for understanding synchronization in pulse-coupled oscillator networks remains absent. In this study, we address this gap by integrating experimental and theoretical approaches. We explore synchronization dynamics through an electronic firefly system, revealing how external illumination disrupts synchronization beyond a critical threshold and affects the process of returning to synchronized states. We propose a minimal mathematical model inspired by laser theory, capturing the delicate balance between synchronizing and desynchronizing forces. Through bifurcation analysis, we identify a range of synchronization regimes – including complete synchronization, partial synchronization, bistability, and explosive synchronization – thereby elucidating the impact of model parameters on these behaviors. This research offers valuable insights into the mechanisms of synchronization in pulse-coupled systems and establishes a theoretical framework that may extend beyond the electronic firefly model, suggesting broader applications in complex networks of oscillators.