Controlling Chaos and Bifurcation by a Delayed Nonlinear Feedback

A method for stabilizing unstable periodic orbits ( UPO) embedded in a chaotic attractor is presented. The conditions for controlling chaos and bifurcation through feeding back a delayed discrete variable are analyzed. The feedback procedure is applicable without knowing a priori the location and the periodicity of the UPO. Our method can be applied not only to the chaotic attractor but also to the situation of bifurcation.