Duffing Oscillator

The Duffing equation ẍ + δẋ + αx + βx³ = γcos(ωt) is a driven nonlinear oscillator. Depending on parameters it shows hardening/softening springs, multiple stable states, period doubling, and strange attractors.

ẍ + δẋ + αx + βx³ = γcos(ωt)
Phase Portrait (x, ẋ)

Parameters

δ (damping)0.30
α (linear)-1.00
β (cubic)1.00
γ (forcing)0.28
ω (frequency)1.20

State

x0.00
0.00
Poincaré section at ωt mod 2π = 0