Estimation of delay times from time series of ring self-oscillatory time-delay systems

Introduction: The problem of delay time estimation in ring self-oscillatory time-delay systems arises in various fields of science and is of great importance in the study of real systems generating chaotic time series. Purpose: To conduct a comparative analysis of the operation of methods for the reconstruction of time-delay systems from chaotic time series in the absence and presence of additive noise. Methods: Methods for estimating the delay time according to the statistics of extrema, using the autocorrelation function and the method of order time asymmetry are used. Based on the latter method, a method is proposed that is focused on estimating the delay times in systems with two delays. Results: We carry out a comparative analysis of the operation of four methods for reconstructing the delay times in self-oscillating time-delay systems from chaotic time series using the example of Ikeda systems with one and two delay times. We demonstrate that in the absence of additive noise, the delay time estimation method based on statistics of extrema is the most accurate one for the case of time series analysis of systems with both one and two delays. In the presence of additive noise, the modified method of order time asymmetry proposed in the work in the case of the analysis of systems with one delay time works no worse than the method of the autocorrelation function and order time asymmetry. In the case of two delay times, the modified order time asymmetry method works better than others. Practical relevance: The described methods can have a practical application in estimating the delay time of self-oscillating systems, yet the level of additive noise can affect the accuracy of the estimate.