Controlling chaos using time delay coordinates via stabilization of periodic orbits

Using time delay coordinates and assuming no a priori knowledge of the dynamical system, we propose a method that stabilizes a desired periodic orbit embedded in a chaotic attractor. Similar to the original control algorithm introduced by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)], the stabilization is done via small time dependent perturbations of an accessible control parameter. The control method is numerically illustrated using both the Ikeda map, which describes the dynamics of a nonlinear laser cavity and the double rotor map which describes a periodically kicked dissipative mechanical system.