EXTRACTING UNSTABLE PERIODIC-ORBITS FROM CHAOTIC TIME-SERIES DATA

A general nonlinear method to extract unstable periodic orbits from ch aotic time series is proposed. By utilizing the estimated local dynami cs along a trajectory, we devise a transformation of the time series d ata such that the transformed data are concentrated on the periodic or bits. Thus, one can extract unstable periodic orbits from a chaotic ti me series by simply looking for peaks in a finite grid approximation o f the distribution function of the transformed data. Our method is dem onstrated using data from both numerical and experimental examples, in cluding neuronal ensemble data from mammalian brain slices. The statis tical significance of the results in the presence of noise is assessed using surrogate data.