Poincaré Map — Driven Pendulum

The damped driven pendulum θ̈ + γθ̇ + sin(θ) = A·cos(ωt) transitions from periodic to chaotic motion as driving amplitude A increases. The Poincaré section samples (θ, θ̇) once per drive cycle, revealing strange attractors and period-doubling cascades.

A (drive amp) 1.15
ω (frequency) 0.667
γ (damping) 0.50
Cycles 500
Left: θ(t) time series  |  Right: Poincaré section — dots = (θ mod 2π, θ̇) at t=nT