Poincaré Map
Period-doubling cascade in the driven Duffing oscillator
Controls
Forcing Amplitude F
0.30
Forcing Freq ω
1.00
Damping δ
0.15
Points to show
500
Reset
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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.