Stabilization of unstable periodic orbits of one-dimensional chaotic maps

Methods have been recently developed for stabilization of periodic orbits that become unstable when the parameter crosses a certain value. However, in a typical case, one-parameter families of nonlinear maps produce periodic orbits that are unstable from the start. In this article, we propose a method for stabilization of such orbits in the one-dimensional case. Results are reported for stabilization of periodic orbits of a quadratic map. © 2002 Plenum Publishing Corporation.