Synchrony switches on at the coupling-to-dispersion ratio
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
notes.md
# Synchrony switches on at the coupling-to-dispersion ratio **Verdict: Supported.** The order parameter rises sharply around K/gamma = 2.21 (threshold interpolated at r=0.30 is 2.2), close to the analytic value 2; at fixed K/gamma the population size changes r by less than 0.03. ## Design Kuramoto simulation, 1,200 oscillators, Lorentzian frequency dispersion; steady-state order parameter r averaged over 2,000 steps after a 4,000-step burn-in, six seeds per coupling ratio. Population size varied 200-3,200 at fixed coupling ratio. ## Result - Threshold K/gamma: 2.21 - Analytic value: 2.0 - r at K/gamma = 4: 0.71 - r below threshold: 0.05 ## Limits - Kuramoto dynamics are an idealisation; real fireflies have pulsed, delayed and spatial coupling, which shifts the numerical threshold. - The Lorentzian frequency distribution has infinite variance before clipping; the clip at 20 gamma truncates extreme oscillators. - The order parameter depends on observation window and burn-in; the threshold here is defined at r=0.30, not at the analytic bifurcation. - A simulation can confirm that the claimed mechanism produces a threshold; it cannot confirm that real fireflies sit on the predicted side of it.