Tool

Duffing oscillator

Mass in a cubic double-well potential, damped and sinusoidally forced. The textbook mechanical resonator that exhibits a period-doubling cascade to chaos.

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α: -1.000

β: 1.000

δ (damping): 0.300

γ (drive amp): 0.500

ω (drive freq): 1.200

Trajectory points: 15,000

Duffing oscillator (driven, damped)

ẍ + δ ẋ + α x + β x³ = γ cos(ω t)

classical double-well: α = −1, β = 1, δ = 0.3, γ = 0.5, ω = 1.2
3rd axis is the drive phase φ = ω t (wrapped to [−π, π]).
A period-doubling cascade to chaos appears as γ grows past ≈ 0.32.

Background at /flows/duffing.

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