With the publication of the seminal paper by Ott, Grebogi and Yorke (OGY) [l] the concept of controlling chaos has become part of the lexicon of physicists and engineers dealing with chaotic nonlinear dynamical systems. The authors showed that by using small, judiciously applied perturbations the unstable periodic orbits, which are dense in a chaotic attractor, could be stabilized. The strength of their approach lies in the absence of the necessity for any a priori analytical model of the chaotic system in order to affect the control. The information required to construct the controlling perturbations can be extracted from experimental time series obtained from the unperturbed system. Since the publication of [l], the OGY controlling algorithm, and numerous variations upon its central concepts, have been implemented numerically and experimentally in a host of nonlinear dynamical systems ranging from lasers and electronic circuits to chemical and biological systems. For excellent review articles see  and the references therein.
Department, Program, or Center
School of Mathematical Sciences (COS)
Nonlinear Optics: Materials, Fundamentals, and Applications (1994) 72-74
RIT – Main Campus