What to Watch
Phase Circle
Bottom-right overlay. Colored dots show each oscillator's phase on the unit circle. When they cluster together = synchronization.
Network Topology
Node colors indicate phase. Edges glow brighter when connected nodes synchronize. The Voronoi background shows each oscillator's territory.
Order Parameter r(t)
Measures global synchronization strength. 0 = complete chaos, 1 = perfect sync. Watch it jump at the critical coupling.
The Model
dθ/dt = ωi + K ∑ sin(θj - θi)
Each oscillator has a natural frequency ωi. Coupling K pulls connected neighbors toward the same phase. Above a critical Kc, a phase transition emerges spontaneously.
Tips for Exploration
Start at K = 0 (chaos) and slowly increase. Watch for the moment r(t) suddenly jumps — that's the phase transition.
At the critical point (~K = 2.5), r(t) fluctuates. This is the edge of order and chaos.
Generate new networks (button below) to see how topology affects synchronization. Dense networks sync easier.
The white dot in the phase circle is the order parameter centroid. When oscillators sync, it moves to the rim.