Deterministic Chaos

Control of Chaos

Here is an outline of the OGY method.

The experimental data are used to build an approximation of the system dynamics.

From this we can find a direction along which iterates move toward the fixed point, even though it is unstable.

By modifying the control parameter and noting how the fixed point changes, we approximate a function relating the position of the fixed point to the control parameter.

Combining these pieces of information, the OGY method predicts how to change the system parameter so one iterate places the state of the system on the direction moving toward the fixed point in the system with the original parameter.

Returning to the original parameter, the system moves toward the fixed point.

Because the fixed point is unstable, and the system is almost surely not exactly on the path leading to the fixed point, eventually the system will move away from the fixed point. When the distance from the fixed point and the system state exceeds some predetermined limit, reapply the control method.

The method requires some linear algebra, but is not too complicated. Here is a simple example.

Return to the method of Ott, Grebogi, and Yorke.