Stabilizing unstable periodic orbits embedded in chaotic attractors
The OGY method (Ott, Grebogi, Yorke 1990) achieves chaos control by applying tiny perturbations to an accessible parameter when the trajectory nears an unstable periodic orbit (UPO) embedded in the chaotic attractor. The key insight: chaotic trajectories visit the neighborhood of every UPO infinitely often, so only small kicks are needed.