Chaos Lab

Continuous flow · dim 3

Duffing oscillator

Driven, damped, cubic-restoring oscillator. The textbook system for studying period-doubling routes to chaos in mechanical resonators and electronic circuits.

Driven, damped Duffing oscillator in (x, ẋ, ωt mod 2π).

Equations

d²x/dt² + δ dx/dt + α x + β x³ = γ cos(ω t)

At a glance

Parametersα = −1, β = 1, δ = 0.3, γ = 0.5, ω = 1.2 (classical double-well)
Chaotic forintermediate driving γ; depends sensitively on all parameters
HistoryDuffing (1918); chaos understood in the 1970s-80s.

Try it

Open the interactive playground at /tools/duffing.

See also

Test your knowledge

8-question flashcard quiz on duffing oscillator

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