Firefly Synchronization

Mirollo-Strogatz 1990: Each firefly has phase φᵢ ∈ [0,1). Flash occurs at φ=1. When a neighbor flashes: φᵢ → f⁻¹(f(φᵢ)+ε) (phase advance). For concave f(φ)=1−e^(−bφ)/(1−e^(−b)): any initial condition reaches global sync. Kuramoto order parameter r = |⟨e^(iθ)⟩|.