Duffing Oscillator: ẍ + δẋ + αx + βx³ = γcos(ωt)
Hardening (β>0)
Softening (β<0)
Limit Cycle
Chaos (period-doubling)
Subharmonic (ω/2)
β
0.50
δ
0.10
γ
0.50
ω
1.00
Reset
Pause
Left: phase portrait (x vs ẋ). Right: time series x(t). Adjust parameters to explore hardening/softening springs, limit cycles, subharmonic response, and the period-doubling route to chaos.