CONTROLLING CHAOS IN A CYCLIC SYSTEM WITH A TIME-DELAYED FEEDBACK

We have shown that a dynamic chaos can be harnessed by Pyragas's schem e of continuous control with a feedback signal in a hybrid Michelson i nterferometer system with a time-delayed feedback. The control was ach ieved when the system was driven into orbits which corresponded to the resonant peaks in the frequency spectrum of the chaotic state. The de lay time in the perturbation signal for control was found to be the pe riod of the unstable periodic orbit embedded in the chaotic attractor, or integer multiples of it. However, the delay time for the control w as occasionally found to be unrelated to the period of the unstable pe riodic orbits. Also, the perturbation gradually became the one with th e same frequency spectrum as that of the controlled signal in the post -transient regime.