ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

#### For citation:

Sysoev I. V., Ponomarenko V. I., Prokhorov M. D. Reconstruction of model equations of networks of oscillators with delay in node dynamics and couplings between them: Review. Izvestiya VUZ. Applied Nonlinear Dynamics, 2019, vol. 27, iss. 4, pp. 13-51. DOI: 10.18500/0869-6632-2019-27-4-13-51

Full text:
Language:
Russian
Article type:
Article
UDC:
530.182

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

Autors:
Sysoev Ilya V., Saratov State University
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotelnikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotelnikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract:

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.

Key words:
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