Detecting and controlling unstable periodic orbits that are not part of a chaotic attractor

A method for controlling unstable periodic orbits (UPOs) that have not been controllable before is presented. The method is based on detecting UPOs that are situated outside the skeleton of a chaotic attractor. The main idea is to exploit flexible parts of the attractor, which under weak external perturbations allow variable excursions of the trajectory away from its originally determined path. After the perturbation, the trajectory of the autonomous system seeks its path back to the chaotic attractor and reveals additional UPOs that are otherwise not used by the system. It is shown that these UPOs can be controlled as easily as the UPOs that form the basic chaotic attractor. The effectiveness of the proposed method is demonstrated on two different chaotic systems with very distinct response abilities to external perturbations. Additionally, some applications of the method in the fields of laser technology, information encoding, and biomedical engineering are discussed.