Defining the controlling conditions of low-dimensional chaotic systems controlled by time-delayed feedback

Based on the occurrence conditions of Hopf bifurcation of a delay system an d corresponding handling methods, we have proposed an analytic method for a chieving the controlling conditions when a low-dimensional chaotic system i s controlled by applying time-delayed feedback on a control variable. Using an analytic method, we can obtain the functional relation of various param eters at the critical points. This method has been applied to some examples and the results show that it is an important means to control chaotic syst ems.