Determination of Parameters of Elements and Coupling Architecture in Ensembles of Coupled Time-Delay Systems from Their Time Series

We propose a method for reconstructing model differential equations with time delay for ensembles of coupled time-delay systems from their time series. The method has made it possible to recover the parameters of elements of the ensemble as well as the architecture and strength of couplings in ensembles of nonidentical systems with delay with an arbitrary number of unidirectional and bidirectional couplings between them. The effectiveness of the method is demonstrated for chaotic and periodic time series of model equations for ensembles of diffusively coupled systems with time delay in the presence of noise, as well as experimental time series for resistively coupled radiotechnical oscillators with delayed feedback.