Parametric Resonance & Period-Doubling Chaos
Periodically driven pitchfork: Poincaré section shows bifurcation cascade
Period: 1 | Lyapunov: —
Driven Duffing oscillator near pitchfork: ẍ + γẋ + x³ − x = A·cos(Ωt).
Left: phase portrait (x, ẋ) with Poincaré section dots (sampled at t=2πn/Ω).
Right: bifurcation diagram — x at Poincaré section vs driving amplitude A.
Period-1 → period-2 → period-4 → chaos via period-doubling (Feigenbaum cascade).