Computing chaotic system control parameters using autoregressive techniques

The sensitivity to initial conditions and orbit complexity which characterize chaotic systems give them a great flexibility to control as compared to non chaotic systems. The motion of chaotic dynamical systems can be converted to periodic motion through small time dependent perturbations, which is a technique developed by Edward Ott, Celso Grebogi, and James York in 1990, known as the OGY technique (E. Ott, 1990). A systematic way to compute the OGY control parameters from a chaotic time series is discussed. It is shown how to use autoregressive modeling to estimate the linear map that describes the system iterative behavior around a fixed point, which is essential for the OGY technique. It is also explained how to experimentally compute the rate of change of a fixed point with respect to a control parameter. And the procedure to be followed according to the order of the controlled periodic orbit is presented. Finally, it is demonstrated how these techniques can be applied to control the chaotic behavior of some typical chaotic system, such as the logistic and Henon maps, to any periodic orbit