RESUMO
An alternative approach of detecting unstable periodic orbits in chaotic time series is proposed using synchronization techniques. A master-slave synchronization scheme is developed, in which the chaotic system drives a system of harmonic oscillators through a proper coupling condition. The proposed scheme is designed so that the power of the coupling signal exhibits notches that drop to zero once the system approaches an unstable orbit yielding an explicit indication of the presence of a periodic motion. The results shows that the proposed approach is particularly suitable in practical situations, where the time series is short and noisy, or it is obtained from high-dimensional chaotic systems.
RESUMO
An effective method of controlling chaos is proposed. The control mechanism of the proposed method can be interpreted as the synchronization of a chaotic system with a system of harmonic oscillators. It is a practically noninvasive method that does not change the solution of dynamical systems, but stabilizes their periodic behavior by applying only small perturbations. The proposed method has fairly simple structure that suggests a clear stabilizing mechanism, and allows a straightforward evaluation of stability properties. This control scheme can be implemented experimentally even if the dynamical system is not analytically known. The efficiency of the proposed method is demonstrated through numerical simulation as well as experimental implementation.