Controlling unstable periodic orbits by a delayed continuous feedback

Abstract

A method is presented for stabilizing unstable periodic orbits of a dynamical system by applying continuous feedback on a control parameter. The feedback signal is proportional to the difference between two values of a dynamical variable, separated by a time equal to the unstable orbit periodicity. This method has been checked numerically and experimentally on the control of the unstable orbits of a ${\mathrm{CO}}_{2}$ laser with modulated losses.