Poincaré Map

Period-doubling cascade in the driven Duffing oscillator

Controls

Period-1
Period-2
Period-4+
Chaotic
Duffing equation:
ẍ − x + x³ = F·cos(ωt) − δẋ

Each dot = state (x, ẋ) sampled once per forcing period. Period-1 → single dot, Period-2 → 2 dots, etc. Increase F to see the cascade into chaos.