HALF-PERIOD DELAYED FEEDBACK-CONTROL FOR DYNAMICAL-SYSTEMS WITH SYMMETRIES

Delayed feedback control (DFC), proposed by Pyragas [Phys. Lett. A 170 , 421 (1992)], is a simple and practical method of controlling chaos i n continuous dynamical systems. However, it had been proved that the D FC has a Limitation; that is, any hyperbolic unstable periodic orbit ( UPO) with an odd number of real characteristic multipliers greater tha n unity can never be stabilized by the DFC. In this paper, to overcome this limitation, we propose a modified DFC, ''half-period delayed fee dback,'' of which the delay time is a half of the period of the UFO. W e apply it to stabilizing self-symmetric directly unstable periodic or bits of the Duffing equation. This modified DFC can also be generalize d to a form stabilizing symmetric periodic orbits in some systems with symmetries such as the Lorenz equation.