Analysis of the Recurrence of Noisy Time Series

Abstract

Abstract—A method based on the use of recurrence plots was proposed for numerical evaluation of the character of the dynamics of noisy time series under conditions where external noise transforms recurrence plots that correspond to qualitatively different dynamic modes such that they become virtually indistinguishable. As demonstrated using the difference logistic map as an example, the method makes it possible to distinguish random fluctuations from deterministic oscillations, including both regular and chaotic oscillations, even when the signal-to-noise ratio is relatively high. An increase in noise level was additionally shown to lead to a convergence of the recurrent properties of regular and chaotic oscillations.