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.
Equations
d²x/dt² + δ dx/dt + α x + β x³ = γ cos(ω t)At a glance
| Parameters | α = −1, β = 1, δ = 0.3, γ = 0.5, ω = 1.2 (classical double-well) |
|---|---|
| Chaotic for | intermediate driving γ; depends sensitively on all parameters |
| History | Duffing (1918); chaos understood in the 1970s-80s. |
Try it
Open the interactive playground at /tools/duffing.