Deterministic Chaos

Control of Chaos

A remarkable feature of the control method developed by Ott, Grebogi, and Yorke is that it can be applied in situations where no underlying model is known.
Often experimental data are sufficient to extract the information necessary for exercising control.
In experiments, we measure some variable, x, of the system at fixed time intervals. Call the measured values x1, x2, x3, ... .
To locate a fixed point, we plot the return map, xn+1 vs xn, and look for where the return map crosses the diagonal.
To locate and stabilize a 2-cycle, use the second return map (plot xn+2 vs xn), and then the same strategy can be applied. The same idea works for longer cycles as well.
The OGY method works this way.

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