Delayed feedback control of chaos by self-adapted delay time

Abstract

We present a novel technique for stabilizing unstable periodic orbits of chaotic systems. It uses a continuous feedback loop in the form of the difference between an actual and a delayed output signal of the system with a variable delay time. This time is chosen to be equal to the interval between the last and the kth previous maximum of the output signal and is changed at every kth maximum. During the procedure, the delay time asymptotically tends to the period of the period-k unstable periodic orbits and the control signal vanishes. The method is illustrated with the help of the Rössler ordinary differential equations and the Mackey-Glass delay differential equations.