OGY Chaos Control — 2D Poincaré-Section Map

This is the 2D companion to the 3D OGY chaos-control simulator: instead of watching the chaotic Rössler flow in three dimensions, it plots the actual mathematical object the controller operates on — the Poincaré return map, a genuinely two-dimensional discrete-time system built from where the flow crosses the plane y = 0. Every dot on the canvas is one real crossing (not a 3D-to-2D projection); the target periodic orbit, the capture window, and the OGY feedback law are all native to this 2D state space. A live integrator still runs the full 3D Rössler system in the background — the control law can only act at those crossings — but nothing here is a flattened render of a 3D scene: this is the reduced-order description that Ott, Grebogi and Yorke's original 1990 method is built around.