Applications of nonlinear time-series analysis in unstable periodic orbits identification

Recently, there has been an extensive interest in research on the analysis and control of chaotic behavior in nonlinear systems. Various control problems can be defined for such systems, such as targeting the trajectories to a desired point, stabilizing unstable periodic orbits etc. The recurrence plot is a two dimensional representation technique that brings out distance correlations in a time series and make it instantly apparent whether a system is periodic or chaotic. In this paper, the proposed method is applied to a nonlinear adaptive control. The stabilization of a chaotic system is achieved through feedback-like control, by using a LTI filter.