Duffing Oscillator Chaos
x'' + δx' + αx + βx³ = γcos(ωt) — Poincaré section, phase portrait, bifurcation
Phase
Poincaré
Bifurc.
Parameters
δ (damping):
0.20
α:
-1.00
β:
1.00
γ (forcing):
0.30
ω (frequency):
1.20
Chaotic preset
Periodic preset
Restart
Bifurcation Diagram
Double-well Duffing:
α<0, β>0 gives two stable equilibria ±√(−α/β).
Chaos:
at γ≈0.3, ω≈1.2 → strange attractor with fractal structure.
Poincaré section:
sample (x, ẋ) once per forcing period — periodic orbit → finite dots, chaos → fractal cloud.