Recovering the attractor: A review of chaotic time-series analysis

Previous applications of chaotic time-series analysis have focussed on either abstract model systems or experimental systems with unknown or poorly understood equations of motion. We present an analysis of experimental time series obtained from a driven nonlinear pendulum with accurately known governing equations. The method of delays provided faithful attractor recoveries in both periodic and chaotic states, showing that high-quality recoveries are possible from experimental time series. Methods for determining the time series' embedding dimension and delay time are also reviewed.