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

Quick quiz

Test yourself on duffing

8 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.The driven, damped Duffing oscillator is famous for:

  2. Q2.The Duffing equation reads:

  3. Q3.For α = −1, β = 1 the unforced potential is:

  4. Q4.What drives the chaos in the forced double-well Duffing?

  5. Q5.George Duffing introduced his oscillator equation in:

  6. Q6.Duffing oscillators model:

  7. Q7.Routes to chaos in Duffing typically include:

  8. Q8.Famous experimental visualisation of the Duffing oscillator:

0 of 8 answered