Identification of Couplings in Adaptive Dynamical Networks of Time-Delayed Feedback Oscillators

Ilya V. Sysoev, Danil D. Kulminskiy, Vladimir I. Ponomarenko and Mikhail D. Prokhorov
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Ilya V. Sysoev: Saratov Branch of the Institute of Radioengineering and Electronics of Russian Academy of Sciences, 38 Zelyonaya Street, 410019 Saratov, Russia
Danil D. Kulminskiy: Saratov Branch of the Institute of Radioengineering and Electronics of Russian Academy of Sciences, 38 Zelyonaya Street, 410019 Saratov, Russia
Vladimir I. Ponomarenko: Saratov Branch of the Institute of Radioengineering and Electronics of Russian Academy of Sciences, 38 Zelyonaya Street, 410019 Saratov, Russia
Mikhail D. Prokhorov: Saratov Branch of the Institute of Radioengineering and Electronics of Russian Academy of Sciences, 38 Zelyonaya Street, 410019 Saratov, Russia

Mathematics, 2021, vol. 9, issue 18, 1-10

Abstract: An approach to solve the inverse problem of the reconstruction of the network of time-delay oscillators from their time series is proposed and studied in the case of the nonstationary connectivity matrix. Adaptive couplings have not been considered yet for this particular reconstruction problem. The problem of coupling identification is reduced to linear optimization of a specially constructed target function. This function is introduced taking into account the continuity of the nonlinear functions of oscillators and does not exploit the mean squared difference between the model and observed time series. The proposed approach allows us to minimize the number of estimated parameters and gives asymptotically unbiased estimates for a large class of nonlinear functions. The approach efficiency is demonstrated for the network composed of time-delayed feedback oscillators with a random architecture of constant and adaptive couplings in the absence of a priori knowledge about the connectivity structure and its evolution. The proposed technique extends the application area of the considered class of methods.

Keywords: adaptive dynamical networks; coupled oscillators; time-delay systems; parameter estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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