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

In this paper, a novel time-delay parameter identification method is proposed based on nonlinear time series analysis combined with network theory. This method accurately reveals the intrinsic time-delay characteristics of the underlying system dynamics. Time-delay parameters are identified from chaotic time series by using two statistical complexity measures defined by two normalized matrices encoding ordinal pattern transition networks of the time series. The proposed method is straightforward to apply and has two prime advantages: it is robust to time series contaminated by dynamical or observational noise, and it is well suited for handling relatively short time series. It increases the upper bound of the possible range of applicable (dynamical) noise intensities by at least two orders of magnitude versus the permutation–information–theory approach. It can also detect two time-delay parameters for relatively short time series in a two-time-delay system, which the delayed mutual information cannot do.