⟨DUFFING OSCILLATOR⟩
Forcing amplitude F
0.30
Forcing frequency ω
1.20
Damping δ
0.20
α (linear spring)
-1.0
β (cubic spring)
1.0
Phase
Poincaré
x(t)
RESET TRAJECTORY
x:
-
ẋ:
-
Phase:
-
Period ratio:
-
Duffing equation:
ẍ + δẋ − αx − βx³ = F cos(ωt). Double-well potential (α<0, β>0) creates two stable equilibria. Chaotic motion emerges from homoclinic tangles. The strange attractor in phase space has fractal dimension ~1.4.