Duffing Oscillator — 2D Phase Portrait & Poincaré Section

ẍ + δẋ + αx + βx³ = γ cos(ωt) — RK4-integrated nonlinear driven spring. Toggle between the phase portrait and the stroboscopic Poincaré section.

α — linear -1.00

β — cubic 1.00

δ — damping 0.30

γ — drive amp. 0.50

ω — drive freq. 1.00

Speed 4×

1.000

0.000

ẋ

0.0

Drive cycles

Poincaré pts

Transient

Regime

Phase Space view (left/default): position x vs velocity ẋ with a fading trail — a closed loop means periodic motion. Poincaré view: stroboscopic samples of (x, ẋ) taken once per drive period T = 2π/ω — a single point means period-1, a small cluster means period doubling, and a scattered fractal cloud means chaos. Both views share the same live RK4 integration; switch anytime without resetting.