OGY Chaos Control – Stabilizing Unstable Periodic Orbits

Ott–Grebogi–Yorke method: stabilize unstable periodic orbits in the Hénon map

Hénon Map: x_{n+1} = 1 − ax_n² + y_n

Parameter a: 1.4 OGY perturbation ε: 0.10 Target orbit period: 1

Chaos control: ON

The OGY method (1990) applies tiny parameter perturbations δa when the trajectory approaches an unstable periodic orbit (UPO). The correction exploits the stable manifold of the UPO. δa = −(λ_u − λ_s)⁻¹(x − x*) / ∂F/∂a Applied only when |x − x*| < ε. The system locks onto the UPO using chaos's own sensitivity.