Time-delay identification from chaotic time series via statistical complexity measures based on ordinal pattern transition networks

Abstract

Abstract In this paper, a methodology based on the nonlinear time series analysis complex network theory to identify time-delay parameters from the chaotic time series is proposed for the first time, to accurately and rapidly reveal the intrinsic time-delay characteristics for the underlying dynamics. More exactly, we discover that time-delay parameters can be identified from chaotic time series by using two statistical complexity measures (SCMs) respectively, which are defined by two normalized ways of the ordinal pattern transition matrix of ordinal pattern transition networks (OPTNs). The prime advantage of the proposed method is straightforward to apply and well robustness to dynamical noises and observational noises. Some other merits were discovered including: A comparative research of the new technique with the permutation-information-theory approach shows that the identifying performance is improved to two orders of magnitude at least for the dynamical Gaussian white noise. And the new method also identifies two time-delay parameters for the condition of relatively short time series, but the traditional delayed mutual information technology cannot.