Thousands of fireflies in one tree flash on the same beat with nobody keeping time. The Kuramoto model explains it with surprisingly cheap ingredients: each oscillator keeps its own slightly different natural frequency and merely nudges its phase toward its neighbours. Across 80 oscillators the degree of synchrony is read off as the order parameter r, equal to 0 when the phases are smeared around the circle and 1 when all of them lock together, and r only leaps up once the coupling crosses a critical threshold. The wider the spread of natural frequencies, the higher that threshold sits.
Thousands of fireflies in one tree flash on the same beat with nobody keeping time. The Kuramoto model explains it with surprisingly cheap ingredients: each oscillator keeps its own slightly different natural frequency and merely nudges its phase toward its neighbours. Across 80 oscillators the degree of synchrony is read off as the order parameter r, equal to 0 when the phases are smeared around the circle and 1 when all of them lock together, and r only leaps up once the coupling crosses a critical threshold. The wider the spread of natural frequencies, the higher that threshold sits.
Related topics in Complexity & Chaos