Firefly Synchronization

Firefly Synchronization (Mirollo & Strogatz 1990): Each firefly is a leaky integrate-and-fire oscillator with phase φ∈[0,1]. When a firefly fires (φ=1), neighbors receive a pulse that advances their phase by ε·Z(φ), where Z is the phase response curve. Over time, all-to-all coupling drives the ensemble to synchrony. The order parameter R = |⟨e^{2πiφ}⟩| measures synchrony: R≈0 is incoherent, R≈1 is fully synchronized. Increase coupling or reduce frequency spread to promote synchronization.