Controlling chaotic dynamical systems using time delay coordinates

Abstract The Ott-Grebogi-Yorke control method is analyzed in the case that the attractor is reconstructed from a time series using time-delay coordinates. It turns out that the control formula of OGY should be modified in order to apply to experimental systems if time-dekay coordinates are used. We reveal that the experimental surface of section map does not only depend on the actual parameter but also on the preceding one. In order to meet this dependence two modifications are introduced which lead to a better performance of the control. To compare their control abilities they are applied to simulations of a Duffing oscillator. The issue of measurement noise is considered.