Reconstruction of model equations of networks of oscillators with delay in node dynamics and couplings between them: Review

The aim of this review is to show the modern level of research in the area of reconstruction of network models from measured time series, for which individual nodes are described by time-delayed equations or there is a delay in coupling. Methods are described for reconstruction of coupling coefficients and functions, nonlinear functions of individual nodes and for detection of superfluous couplings. The techniques for delay time detection are considered separately due to their choice is crucial for success of entire reconstruction procedure. There presented the results of reconstruction from times series of model oscillators with different nonlinear functions, coupling fucntions, with number of nodes in a netwoks ranging widely (from 3 to tens of nodes). In addition, the results of reconstruction of models from different radiophysical experiments are presented. The advantages and shortcomings of proposed approaches are discussed in comparison with other known from literature methods of coupling estimation. The effects of time series length, the amount of a priori information, measurement noise, calculation errors on method efficiency are considered.