Controlling chaos 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 Ott, Grebogi, and Yorke should be modified in order to apply to experimental systems if time delay coordinates are used. We reveal that the experimental surface of section map depends not only 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.