OGY Chaos Control — Stabilizing a Hidden Periodic Orbit

Chaos is not pure noise — buried inside every strange attractor is a dense scaffold of unstable periodic orbits, and the OGY method (Ott, Grebogi & Yorke, 1990) shows how to ride one of them without fighting the chaos at all. This simulator integrates the chaotic Rössler system in real time, numerically discovers one of its unstable periodic orbits by hunting for close returns on a Poincaré section, linearizes the local dynamics to compute the exact feedback law, and applies it as tiny, occasional nudges to a single parameter whenever the trajectory drifts near that orbit. Toggle control on and off, tighten or loosen the capture window, and kick the system to watch it find its way back — the whole control loop, from orbit discovery to the linear feedback gain, is computed live in the browser rather than hard-coded.